Properties

Label 42135g
Number of curves $1$
Conductor $42135$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 42135g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
42135.h1 42135g1 \([0, 1, 1, -35, -91]\) \(1736704/45\) \(126405\) \([]\) \(3456\) \(-0.23916\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 42135g1 has rank \(1\).

Complex multiplication

The elliptic curves in class 42135g do not have complex multiplication.

Modular form 42135.2.a.g

sage: E.q_eigenform(10)
 
\(q + q^{3} - 2 q^{4} + q^{5} + q^{9} + 4 q^{11} - 2 q^{12} + 4 q^{13} + q^{15} + 4 q^{16} - 2 q^{17} - q^{19} + O(q^{20})\) Copy content Toggle raw display