Properties

Label 5070.p
Number of curves $1$
Conductor $5070$
CM no
Rank $0$

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

Elliptic curves in class 5070.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5070.p1 5070n1 \([1, 1, 1, 39939, 1301139]\) \(41689615345255319/28343520000000\) \(-4790054880000000\) \([]\) \(40656\) \(1.6974\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 5070.p1 has rank \(0\).

Complex multiplication

The elliptic curves in class 5070.p do not have complex multiplication.

Modular form 5070.2.a.p

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