Properties

Label 70602x
Number of curves $1$
Conductor $70602$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("x1")
 
E.isogeny_class()
 

Elliptic curves in class 70602x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
70602.n1 70602x1 \([1, 1, 1, -53827, 26627105]\) \(-3630961153/62487936\) \(-296824209804936576\) \([]\) \(940800\) \(2.0338\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 70602x1 has rank \(1\).

Complex multiplication

The elliptic curves in class 70602x do not have complex multiplication.

Modular form 70602.2.a.x

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - 3 q^{5} - q^{6} + q^{7} + q^{8} + q^{9} - 3 q^{10} - q^{12} + 5 q^{13} + q^{14} + 3 q^{15} + q^{16} + q^{17} + q^{18} + q^{19} + O(q^{20})\) Copy content Toggle raw display