Properties

Label 702.e
Number of curves 11
Conductor 702702
CM no
Rank 11

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 702.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
702.e1 702a1 [1,1,0,9,19][1, -1, 0, -9, -19] 3176523/5408-3176523/5408 146016-146016 [][] 120120 0.31841-0.31841 Γ0(N)\Gamma_0(N)-optimal

Rank

sage: E.rank()
 

The elliptic curve 702.e1 has rank 11.

Complex multiplication

The elliptic curves in class 702.e do not have complex multiplication.

Modular form 702.2.a.e

sage: E.q_eigenform(10)
 
qq2+q4+q55q7q8q10+5q11q13+5q14+q166q176q19+O(q20)q - q^{2} + q^{4} + q^{5} - 5 q^{7} - q^{8} - q^{10} + 5 q^{11} - q^{13} + 5 q^{14} + q^{16} - 6 q^{17} - 6 q^{19} + O(q^{20}) Copy content Toggle raw display