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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 100011.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
100011.a1 | 100011e1 | \([0, 1, 1, 1070, 7408]\) | \(135353378115584/99811078011\) | \(-99811078011\) | \([]\) | \(121968\) | \(0.79881\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 100011.a1 has rank \(1\).
Complex multiplication
The elliptic curves in class 100011.a do not have complex multiplication.Modular form 100011.2.a.a
sage: E.q_eigenform(10)