Properties

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

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Show commands: SageMath
E = EllipticCurve("bg1")
 
E.isogeny_class()
 

Elliptic curves in class 70602bg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
70602.be1 70602bg1 \([1, 0, 0, -494659, 314997185]\) \(-194218207880195897/509703742291968\) \(-35129291622504726528\) \([]\) \(2185920\) \(2.4380\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 70602bg1 has rank \(1\).

Complex multiplication

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

Modular form 70602.2.a.bg

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