Properties

Label 70021.a
Number of curves $1$
Conductor $70021$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 70021.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
70021.a1 70021a1 \([1, 0, 0, 2547, -63764]\) \(15531437375/24017203\) \(-2825599915747\) \([]\) \(94080\) \(1.0744\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 70021.a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 70021.a do not have complex multiplication.

Modular form 70021.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{2} - 2 q^{3} - q^{4} + 2 q^{6} + 3 q^{8} + q^{9} + 6 q^{11} + 2 q^{12} + 2 q^{13} - q^{16} + 4 q^{17} - q^{18} + 4 q^{19} + O(q^{20})\) Copy content Toggle raw display