Properties

Label 412224v
Number of curves $1$
Conductor $412224$
CM no
Rank $2$

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Show commands: SageMath
E = EllipticCurve("v1")
 
E.isogeny_class()
 

Elliptic curves in class 412224v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
412224.v1 412224v1 \([0, -1, 0, -1845, 31509]\) \(-678653722624/9912699\) \(-10150603776\) \([]\) \(199680\) \(0.72435\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 412224v1 has rank \(2\).

Complex multiplication

The elliptic curves in class 412224v do not have complex multiplication.

Modular form 412224.2.a.v

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} + q^{7} + q^{9} - 2 q^{11} - 3 q^{13} - q^{15} - q^{17} - q^{19} + O(q^{20})\) Copy content Toggle raw display