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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 400710g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
400710.g2 | 400710g1 | \([1, 1, 0, -368, -35028]\) | \(-117649/11100\) | \(-522209279100\) | \([2]\) | \(570240\) | \(0.92802\) | \(\Gamma_0(N)\)-optimal* |
400710.g1 | 400710g2 | \([1, 1, 0, -18418, -962798]\) | \(14688124849/123210\) | \(5796522998010\) | \([2]\) | \(1140480\) | \(1.2746\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 400710g have rank \(0\).
Complex multiplication
The elliptic curves in class 400710g do not have complex multiplication.Modular form 400710.2.a.g
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.