Properties

Label 42042e
Number of curves $1$
Conductor $42042$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 42042e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
42042.e1 42042e1 \([1, 1, 0, 30992, -1579136]\) \(571039705271/520401024\) \(-3000008343556224\) \([]\) \(263424\) \(1.6571\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 42042e1 has rank \(0\).

Complex multiplication

The elliptic curves in class 42042e do not have complex multiplication.

Modular form 42042.2.a.e

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} - q^{8} + q^{9} + q^{10} + q^{11} - q^{12} - q^{13} + q^{15} + q^{16} + 7 q^{17} - q^{18} + O(q^{20})\) Copy content Toggle raw display