Properties

Label 42350ca
Number of curves $1$
Conductor $42350$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("ca1")
 
E.isogeny_class()
 

Elliptic curves in class 42350ca

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
42350.db1 42350ca1 \([1, -1, 1, -543555, -166629053]\) \(-1026590625/100352\) \(-1736129780000000000\) \([]\) \(1570800\) \(2.2408\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 42350ca1 has rank \(1\).

Complex multiplication

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

Modular form 42350.2.a.ca

sage: E.q_eigenform(10)
 
\(q + q^{2} + 3 q^{3} + q^{4} + 3 q^{6} - q^{7} + q^{8} + 6 q^{9} + 3 q^{12} - 6 q^{13} - q^{14} + q^{16} - q^{17} + 6 q^{18} + 3 q^{19} + O(q^{20})\) Copy content Toggle raw display