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SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 56784bf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 56784.m1 | 56784bf1 | \([0, -1, 0, 6867259, 22253052717]\) | \(1811564780171264/11870974573731\) | \(-234696404628504389136384\) | \([]\) | \(4515840\) | \(3.1661\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 56784bf1 has rank \(0\).
Complex multiplication
The elliptic curves in class 56784bf do not have complex multiplication.Modular form 56784.2.a.bf
sage: E.q_eigenform(10)