Properties

Label 7942.a
Number of curves $1$
Conductor $7942$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 7942.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7942.a1 7942k1 \([1, -1, 0, -2053, 42739]\) \(-20346417/4598\) \(-216316960838\) \([]\) \(20160\) \(0.89504\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 7942.a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 7942.a do not have complex multiplication.

Modular form 7942.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{2} - 3 q^{3} + q^{4} - 2 q^{5} + 3 q^{6} + q^{7} - q^{8} + 6 q^{9} + 2 q^{10} + q^{11} - 3 q^{12} + 7 q^{13} - q^{14} + 6 q^{15} + q^{16} - 3 q^{17} - 6 q^{18} + O(q^{20})\) Copy content Toggle raw display