Properties

Label 70805.s
Number of curves $1$
Conductor $70805$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("s1")
 
E.isogeny_class()
 

Elliptic curves in class 70805.s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
70805.s1 70805c1 \([1, 0, 0, -85261, -12166274]\) \(-14161/5\) \(-24202006774890245\) \([]\) \(481032\) \(1.8548\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 70805.s1 has rank \(1\).

Complex multiplication

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

Modular form 70805.2.a.s

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