Properties

Label 429429i
Number of curves $1$
Conductor $429429$
CM no
Rank $2$

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

Elliptic curves in class 429429i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
429429.i1 429429i1 \([0, -1, 1, -6468700, -44781613680]\) \(-1593413632/45196767\) \(-849089854809530742459051\) \([]\) \(97044480\) \(3.2720\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 429429i1 has rank \(2\).

Complex multiplication

The elliptic curves in class 429429i do not have complex multiplication.

Modular form 429429.2.a.i

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