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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 5040.bd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5040.bd1 | 5040bp1 | \([0, 0, 0, 288, 5724]\) | \(14155776/84035\) | \(-15682947840\) | \([]\) | \(3360\) | \(0.63824\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 5040.bd1 has rank \(1\).
Complex multiplication
The elliptic curves in class 5040.bd do not have complex multiplication.Modular form 5040.2.a.bd
sage: E.q_eigenform(10)