Properties

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

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Show commands: SageMath
E = EllipticCurve("p1")
 
E.isogeny_class()
 

Elliptic curves in class 70805.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
70805.p1 70805bq1 \([1, 1, 1, -50870, 4379220]\) \(6084487/25\) \(59817120056575\) \([]\) \(215424\) \(1.4991\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 70805.p1 has rank \(2\).

Complex multiplication

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

Modular form 70805.2.a.p

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