Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("i1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 5070.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5070.i1 5070j1 \([1, 0, 1, -836554, -294572068]\) \(-79370312059129/12960\) \(-10571870144160\) \([]\) \(87360\) \(1.9006\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 5070.i1 has rank \(0\).

Complex multiplication

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

Modular form 5070.2.a.i

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