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SageMath
E = EllipticCurve("dr1")
E.isogeny_class()
Elliptic curves in class 106722dr
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
106722.p1 | 106722dr1 | \([1, -1, 0, -508041, 193052173]\) | \(-1397395501513/740710656\) | \(-7686873449566730496\) | \([]\) | \(2949120\) | \(2.3280\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 106722dr1 has rank \(0\).
Complex multiplication
The elliptic curves in class 106722dr do not have complex multiplication.Modular form 106722.2.a.dr
sage: E.q_eigenform(10)