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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 1012.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1012.d1 | 1012a1 | \([0, 1, 0, -884166, 319707497]\) | \(-4777554520541237119744/49850049369527\) | \(-797600789912432\) | \([]\) | \(13776\) | \(2.0164\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 1012.d1 has rank \(0\).
Complex multiplication
The elliptic curves in class 1012.d do not have complex multiplication.Modular form 1012.2.a.d
sage: E.q_eigenform(10)