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SageMath
E = EllipticCurve("gd1")
E.isogeny_class()
Elliptic curves in class 121275gd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
121275.f1 | 121275gd1 | \([0, 0, 1, -454125, -98202344]\) | \(148455501824/26198073\) | \(1827776104751953125\) | \([]\) | \(2280960\) | \(2.2237\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 121275gd1 has rank \(0\).
Complex multiplication
The elliptic curves in class 121275gd do not have complex multiplication.Modular form 121275.2.a.gd
sage: E.q_eigenform(10)