Properties

Label 37296bd
Number of curves $2$
Conductor $37296$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bd1")
 
E.isogeny_class()
 

Elliptic curves in class 37296bd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
37296.cm1 37296bd1 \([0, 0, 0, -151938, -22795425]\) \(33256413948450816/2481997\) \(28950013008\) \([2]\) \(156672\) \(1.4570\) \(\Gamma_0(N)\)-optimal
37296.cm2 37296bd2 \([0, 0, 0, -151623, -22894650]\) \(-2065624967846736/17960084863\) \(-3351782877472512\) \([2]\) \(313344\) \(1.8036\)  

Rank

sage: E.rank()
 

The elliptic curves in class 37296bd have rank \(1\).

Complex multiplication

The elliptic curves in class 37296bd do not have complex multiplication.

Modular form 37296.2.a.bd

sage: E.q_eigenform(10)
 
\(q + 4 q^{5} + q^{7} - 4 q^{11} - 4 q^{13} - 2 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.