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SageMath
E = EllipticCurve("hd1")
E.isogeny_class()
Elliptic curves in class 84672hd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
84672.jj1 | 84672hd1 | \([0, 0, 0, -294, -2058]\) | \(-13824\) | \(-203297472\) | \([]\) | \(31680\) | \(0.34378\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 84672hd1 has rank \(1\).
Complex multiplication
The elliptic curves in class 84672hd do not have complex multiplication.Modular form 84672.2.a.hd
sage: E.q_eigenform(10)