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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 76440r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
76440.s1 | 76440r1 | \([0, -1, 0, 476215, -83396403]\) | \(396555344454656/328867205355\) | \(-9904869847759461120\) | \([]\) | \(1995840\) | \(2.3327\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 76440r1 has rank \(1\).
Complex multiplication
The elliptic curves in class 76440r do not have complex multiplication.Modular form 76440.2.a.r
sage: E.q_eigenform(10)