Properties

Label 176400.lm
Number of curves $8$
Conductor $176400$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("lm1")
 
E.isogeny_class()
 

Elliptic curves in class 176400.lm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
176400.lm1 176400fm8 \([0, 0, 0, -1137960075, -9295716487750]\) \(29689921233686449/10380965400750\) \(56981448618082431408000000000\) \([2]\) \(127401984\) \(4.2192\)  
176400.lm2 176400fm5 \([0, 0, 0, -1016244075, -12469387099750]\) \(21145699168383889/2593080\) \(14233498434731520000000\) \([2]\) \(42467328\) \(3.6698\)  
176400.lm3 176400fm6 \([0, 0, 0, -476460075, 3896578012250]\) \(2179252305146449/66177562500\) \(363250741303044000000000000\) \([2, 2]\) \(63700992\) \(3.8726\)  
176400.lm4 176400fm3 \([0, 0, 0, -472932075, 3958639060250]\) \(2131200347946769/2058000\) \(11296427329152000000000\) \([2]\) \(31850496\) \(3.5260\)  
176400.lm5 176400fm2 \([0, 0, 0, -63684075, -193746379750]\) \(5203798902289/57153600\) \(313717924683878400000000\) \([2, 2]\) \(21233664\) \(3.3233\)  
176400.lm6 176400fm4 \([0, 0, 0, -14292075, -486591547750]\) \(-58818484369/18600435000\) \(-102098378167208640000000000\) \([2]\) \(42467328\) \(3.6698\)  
176400.lm7 176400fm1 \([0, 0, 0, -7236075, 2636212250]\) \(7633736209/3870720\) \(21246504952135680000000\) \([2]\) \(10616832\) \(2.9767\) \(\Gamma_0(N)\)-optimal
176400.lm8 176400fm7 \([0, 0, 0, 128591925, 13116965440250]\) \(42841933504271/13565917968750\) \(-74463754366968750000000000000\) \([2]\) \(127401984\) \(4.2192\)  

Rank

sage: E.rank()
 

The elliptic curves in class 176400.lm have rank \(0\).

Complex multiplication

The elliptic curves in class 176400.lm do not have complex multiplication.

Modular form 176400.2.a.lm

sage: E.q_eigenform(10)
 
\(q + 2 q^{13} + 6 q^{17} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rrrrrrrr} 1 & 3 & 2 & 4 & 6 & 12 & 12 & 4 \\ 3 & 1 & 6 & 12 & 2 & 4 & 4 & 12 \\ 2 & 6 & 1 & 2 & 3 & 6 & 6 & 2 \\ 4 & 12 & 2 & 1 & 6 & 12 & 3 & 4 \\ 6 & 2 & 3 & 6 & 1 & 2 & 2 & 6 \\ 12 & 4 & 6 & 12 & 2 & 1 & 4 & 3 \\ 12 & 4 & 6 & 3 & 2 & 4 & 1 & 12 \\ 4 & 12 & 2 & 4 & 6 & 3 & 12 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.