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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 235950b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
235950.b2 | 235950b1 | \([1, 1, 0, -1076660, 429546000]\) | \(623295446073461/5458752\) | \(1208814018984000\) | \([2]\) | \(4300800\) | \(2.0609\) | \(\Gamma_0(N)\)-optimal |
235950.b1 | 235950b2 | \([1, 1, 0, -1100860, 409193800]\) | \(666276475992821/58199166792\) | \(12887921765150289000\) | \([2]\) | \(8601600\) | \(2.4075\) |
Rank
sage: E.rank()
The elliptic curves in class 235950b have rank \(1\).
Complex multiplication
The elliptic curves in class 235950b do not have complex multiplication.Modular form 235950.2.a.b
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.