Properties

Label 70602.z
Number of curves $1$
Conductor $70602$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("z1")
 
E.isogeny_class()
 

Elliptic curves in class 70602.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
70602.z1 70602y1 \([1, 1, 1, -5540611, 5832037931]\) \(-3959985141923329/804085973082\) \(-3819492190865420040762\) \([]\) \(7862400\) \(2.8636\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 70602.z1 has rank \(1\).

Complex multiplication

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

Modular form 70602.2.a.z

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} + 4 q^{5} - q^{6} + q^{7} + q^{8} + q^{9} + 4 q^{10} + q^{11} - q^{12} + 4 q^{13} + q^{14} - 4 q^{15} + q^{16} - 2 q^{17} + q^{18} - 5 q^{19} + O(q^{20})\) Copy content Toggle raw display