Properties

Label 70805z
Number of curves $1$
Conductor $70805$
CM no
Rank $2$

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

Elliptic curves in class 70805z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
70805.x1 70805z1 \([0, 0, 1, -11662, 173472]\) \(6193152/3125\) \(88507710353125\) \([]\) \(282240\) \(1.3688\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 70805z1 has rank \(2\).

Complex multiplication

The elliptic curves in class 70805z do not have complex multiplication.

Modular form 70805.2.a.z

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