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SageMath
E = EllipticCurve("bv1")
E.isogeny_class()
Elliptic curves in class 392784bv
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
392784.bv2 | 392784bv1 | \([0, 1, 0, -3544, -338668]\) | \(-10218313/96192\) | \(-46353992122368\) | \([2]\) | \(995328\) | \(1.3047\) | \(\Gamma_0(N)\)-optimal |
392784.bv1 | 392784bv2 | \([0, 1, 0, -97624, -11741164]\) | \(213525509833/669336\) | \(322546528518144\) | \([2]\) | \(1990656\) | \(1.6512\) |
Rank
sage: E.rank()
The elliptic curves in class 392784bv have rank \(1\).
Complex multiplication
The elliptic curves in class 392784bv do not have complex multiplication.Modular form 392784.2.a.bv
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.