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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 426888.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
426888.i1 | 426888i2 | \([0, 0, 0, -2152227, 1200681790]\) | \(3543122/49\) | \(15247474358597978112\) | \([2]\) | \(13271040\) | \(2.4865\) | \(\Gamma_0(N)\)-optimal* |
426888.i2 | 426888i1 | \([0, 0, 0, -17787, 50218630]\) | \(-4/7\) | \(-1089105311328427008\) | \([2]\) | \(6635520\) | \(2.1400\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 426888.i have rank \(2\).
Complex multiplication
The elliptic curves in class 426888.i do not have complex multiplication.Modular form 426888.2.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.