Properties

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

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 70602.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
70602.c1 70602b1 \([1, 1, 0, -71477, -33539667]\) \(-8502154921/97203456\) \(-461726548585456896\) \([]\) \(967680\) \(2.0714\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 70602.c1 has rank \(1\).

Complex multiplication

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

Modular form 70602.2.a.c

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