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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 424830.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
424830.i1 | 424830i2 | \([1, 1, 0, -2211493, -1266670103]\) | \(2069406085491737/160744500\) | \(92911854020296500\) | \([2]\) | \(9437184\) | \(2.3034\) | \(\Gamma_0(N)\)-optimal* |
424830.i2 | 424830i1 | \([1, 1, 0, -128993, -22584603]\) | \(-410669451737/141750000\) | \(-81932851869750000\) | \([2]\) | \(4718592\) | \(1.9568\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 424830.i have rank \(0\).
Complex multiplication
The elliptic curves in class 424830.i do not have complex multiplication.Modular form 424830.2.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.