Properties

Label 70602f
Number of curves $1$
Conductor $70602$
CM no
Rank $2$

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 70602f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
70602.h1 70602f1 \([1, 0, 1, -106909114, 434064874700]\) \(-28448852731909216489/672475186714464\) \(-3194327236379642302441824\) \([]\) \(14112000\) \(3.4884\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 70602f1 has rank \(2\).

Complex multiplication

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

Modular form 70602.2.a.f

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