Properties

Label 297024.eb
Number of curves $1$
Conductor $297024$
CM no
Rank $2$

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Show commands: SageMath
E = EllipticCurve("eb1")
 
E.isogeny_class()
 

Elliptic curves in class 297024.eb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
297024.eb1 297024eb1 \([0, 1, 0, -57, 2421]\) \(-325660672/40000779\) \(-2560049856\) \([]\) \(176640\) \(0.48473\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 297024.eb1 has rank \(2\).

Complex multiplication

The elliptic curves in class 297024.eb do not have complex multiplication.

Modular form 297024.2.a.eb

sage: E.q_eigenform(10)
 
\(q + q^{3} - 3 q^{5} - q^{7} + q^{9} - 6 q^{11} + q^{13} - 3 q^{15} - q^{17} - q^{19} + O(q^{20})\) Copy content Toggle raw display