Properties

Label 18480bm
Number of curves $8$
Conductor $18480$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bm1")
 
E.isogeny_class()
 

Elliptic curves in class 18480bm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
18480.l8 18480bm1 \([0, -1, 0, 25424, -203840]\) \(443688652450511/260789760000\) \(-1068194856960000\) \([2]\) \(82944\) \(1.5731\) \(\Gamma_0(N)\)-optimal
18480.l7 18480bm2 \([0, -1, 0, -102576, -1535040]\) \(29141055407581489/16604321025600\) \(68011298920857600\) \([2, 2]\) \(165888\) \(1.9197\)  
18480.l6 18480bm3 \([0, -1, 0, -324016, 78049216]\) \(-918468938249433649/109183593750000\) \(-447216000000000000\) \([2]\) \(248832\) \(2.1224\)  
18480.l4 18480bm4 \([0, -1, 0, -1200176, -504674880]\) \(46676570542430835889/106752955783320\) \(437260106888478720\) \([2]\) \(331776\) \(2.2663\)  
18480.l5 18480bm5 \([0, -1, 0, -1052976, 414360000]\) \(31522423139920199089/164434491947880\) \(673523679018516480\) \([2]\) \(331776\) \(2.2663\)  
18480.l3 18480bm6 \([0, -1, 0, -5324016, 4730049216]\) \(4074571110566294433649/48828650062500\) \(200002150656000000\) \([2, 2]\) \(497664\) \(2.4690\)  
18480.l2 18480bm7 \([0, -1, 0, -5464016, 4468305216]\) \(4404531606962679693649/444872222400201750\) \(1822196622951226368000\) \([2]\) \(995328\) \(2.8156\)  
18480.l1 18480bm8 \([0, -1, 0, -85184016, 302639793216]\) \(16689299266861680229173649/2396798250\) \(9817285632000\) \([2]\) \(995328\) \(2.8156\)  

Rank

sage: E.rank()
 

The elliptic curves in class 18480bm have rank \(1\).

Complex multiplication

The elliptic curves in class 18480bm do not have complex multiplication.

Modular form 18480.2.a.bm

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} - q^{7} + q^{9} + q^{11} + 2 q^{13} + q^{15} + 6 q^{17} + 4 q^{19} + O(q^{20})\) 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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.