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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)
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.