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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 12138.x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
12138.x1 | 12138bd1 | \([1, 0, 0, -636962, -200564796]\) | \(-1184052061112257/34349180544\) | \(-829105715474257536\) | \([]\) | \(241920\) | \(2.2175\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 12138.x1 has rank \(0\).
Complex multiplication
The elliptic curves in class 12138.x do not have complex multiplication.Modular form 12138.2.a.x
sage: E.q_eigenform(10)