Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("ba1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 37296ba

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
37296.cc2 37296ba1 \([0, 0, 0, 141, -28478]\) \(415292/469567\) \(-350529887232\) \([2]\) \(41472\) \(0.89422\) \(\Gamma_0(N)\)-optimal
37296.cc1 37296ba2 \([0, 0, 0, -13179, -569270]\) \(169556172914/4353013\) \(6499013584896\) \([2]\) \(82944\) \(1.2408\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 37296.2.a.ba

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