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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 400710.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
400710.i1 | 400710i2 | \([1, 1, 0, -3418677, 2431537149]\) | \(93923986054560481/16028400\) | \(754070199020400\) | \([2]\) | \(8110080\) | \(2.2535\) | \(\Gamma_0(N)\)-optimal* |
400710.i2 | 400710i1 | \([1, 1, 0, -212997, 38176461]\) | \(-22715680520161/299646720\) | \(-14097143931160320\) | \([2]\) | \(4055040\) | \(1.9069\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 400710.i have rank \(1\).
Complex multiplication
The elliptic curves in class 400710.i do not have complex multiplication.Modular form 400710.2.a.i
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.