Properties

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

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Show commands: SageMath
E = EllipticCurve("h1")
 
E.isogeny_class()
 

Elliptic curves in class 42135h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
42135.g1 42135h1 \([0, 1, 1, -621725, -189502969]\) \(-1199124250624/4471875\) \(-99116252423746875\) \([]\) \(505440\) \(2.1212\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 42135h1 has rank \(1\).

Complex multiplication

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

Modular form 42135.2.a.h

sage: E.q_eigenform(10)
 
\(q + q^{3} - 2 q^{4} + q^{5} - 2 q^{7} + q^{9} - 4 q^{11} - 2 q^{12} + q^{15} + 4 q^{16} + 5 q^{17} + 4 q^{19} + O(q^{20})\) Copy content Toggle raw display