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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 8048c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
8048.i1 | 8048c1 | \([0, 1, 0, 12, -4]\) | \(686000/503\) | \(-128768\) | \([]\) | \(768\) | \(-0.33122\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 8048c1 has rank \(0\).
Complex multiplication
The elliptic curves in class 8048c do not have complex multiplication.Modular form 8048.2.a.c
sage: E.q_eigenform(10)