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SageMath
E = EllipticCurve("bv1")
E.isogeny_class()
Elliptic curves in class 101430.bv
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
101430.bv1 | 101430m1 | \([1, -1, 0, -2172631344, -16296617550592]\) | \(489781415227546051766883/233890092903563264000\) | \(541615842234042702247231488000\) | \([2]\) | \(148635648\) | \(4.3993\) | \(\Gamma_0(N)\)-optimal |
101430.bv2 | 101430m2 | \([1, -1, 0, 7798343376, -123957219992320]\) | \(22649115256119592694355357/15973509811739648000000\) | \(-36989621333325446513366016000000\) | \([2]\) | \(297271296\) | \(4.7458\) |
Rank
sage: E.rank()
The elliptic curves in class 101430.bv have rank \(1\).
Complex multiplication
The elliptic curves in class 101430.bv do not have complex multiplication.Modular form 101430.2.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 LMFDB 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 LMFDB labels.