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Properties

Label 1470.m
Number of curves $8$
Conductor $1470$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("m1")
 
E.isogeny_class()
 

Elliptic curves in class 1470.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1470.m1 1470m7 \([1, 1, 1, -316100, -43167433]\) \(29689921233686449/10380965400750\) \(1221310198432836750\) \([2]\) \(27648\) \(2.1720\)  
1470.m2 1470m4 \([1, 1, 1, -282290, -57846265]\) \(21145699168383889/2593080\) \(305073268920\) \([2]\) \(9216\) \(1.6227\)  
1470.m3 1470m6 \([1, 1, 1, -132350, 17984567]\) \(2179252305146449/66177562500\) \(7785724050562500\) \([2, 2]\) \(13824\) \(1.8254\)  
1470.m4 1470m3 \([1, 1, 1, -131370, 18272295]\) \(2131200347946769/2058000\) \(242121642000\) \([4]\) \(6912\) \(1.4788\)  
1470.m5 1470m2 \([1, 1, 1, -17690, -904345]\) \(5203798902289/57153600\) \(6724063886400\) \([2, 2]\) \(4608\) \(1.2761\)  
1470.m6 1470m5 \([1, 1, 1, -3970, -2254393]\) \(-58818484369/18600435000\) \(-2188322577315000\) \([2]\) \(9216\) \(1.6227\)  
1470.m7 1470m1 \([1, 1, 1, -2010, 11367]\) \(7633736209/3870720\) \(455386337280\) \([4]\) \(2304\) \(0.92953\) \(\Gamma_0(N)\)-optimal
1470.m8 1470m8 \([1, 1, 1, 35720, 60741575]\) \(42841933504271/13565917968750\) \(-1596016683105468750\) \([2]\) \(27648\) \(2.1720\)  

Rank

sage: E.rank()
 

The elliptic curves in class 1470.m have rank \(0\).

Complex multiplication

The elliptic curves in class 1470.m do not have complex multiplication.

Modular form 1470.2.a.m

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} + q^{8} + q^{9} + q^{10} - q^{12} - 2 q^{13} - q^{15} + q^{16} + 6 q^{17} + q^{18} + 4 q^{19} + O(q^{20})\) 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.