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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 69300.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
69300.e1 | 69300o1 | \([0, 0, 0, -4604973000, -120278722387500]\) | \(-799965408846201776676864/128959272851717\) | \(-1740950183498179500000000\) | \([]\) | \(31749120\) | \(4.0536\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 69300.e1 has rank \(1\).
Complex multiplication
The elliptic curves in class 69300.e do not have complex multiplication.Modular form 69300.2.a.e
sage: E.q_eigenform(10)