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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 363090.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
363090.a1 | 363090a1 | \([1, 1, 0, -246838, -38030432]\) | \(41217358701007/8452957500\) | \(341107324942702500\) | \([2]\) | \(8945664\) | \(2.0797\) | \(\Gamma_0(N)\)-optimal |
363090.a2 | 363090a2 | \([1, 1, 0, 524912, -227417882]\) | \(396368892374993/784115122050\) | \(-31641873477962734350\) | \([2]\) | \(17891328\) | \(2.4262\) |
Rank
sage: E.rank()
The elliptic curves in class 363090.a have rank \(0\).
Complex multiplication
The elliptic curves in class 363090.a do not have complex multiplication.Modular form 363090.2.a.a
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.