Properties

Label 42350i
Number of curves $1$
Conductor $42350$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 42350i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
42350.k1 42350i1 \([1, 1, 0, -996250, 382416500]\) \(-57839429434456681/16470860000\) \(-31140219687500000\) \([]\) \(645120\) \(2.1454\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 42350i1 has rank \(0\).

Complex multiplication

The elliptic curves in class 42350i do not have complex multiplication.

Modular form 42350.2.a.i

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} - q^{7} - q^{8} - 2 q^{9} - q^{12} + 3 q^{13} + q^{14} + q^{16} + 2 q^{18} - 3 q^{19} + O(q^{20})\) Copy content Toggle raw display