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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 935b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
935.b1 | 935b1 | \([0, 1, 1, -13155, 576381]\) | \(-251784668965666816/353546875\) | \(-353546875\) | \([3]\) | \(1464\) | \(0.91264\) | \(\Gamma_0(N)\)-optimal |
935.b2 | 935b2 | \([0, 1, 1, -9655, 893306]\) | \(-99546392709922816/289614925147075\) | \(-289614925147075\) | \([]\) | \(4392\) | \(1.4619\) |
Rank
sage: E.rank()
The elliptic curves in class 935b have rank \(0\).
Complex multiplication
The elliptic curves in class 935b do not have complex multiplication.Modular form 935.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.