Properties

Label 68400ew
Number of curves $1$
Conductor $68400$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("ew1")
 
E.isogeny_class()
 

Elliptic curves in class 68400ew

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
68400.b1 68400ew1 \([0, 0, 0, -171675, 29234250]\) \(-11993263569/972800\) \(-45386956800000000\) \([]\) \(709632\) \(1.9424\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 68400ew1 has rank \(1\).

Complex multiplication

The elliptic curves in class 68400ew do not have complex multiplication.

Modular form 68400.2.a.ew

sage: E.q_eigenform(10)
 
\(q - 5 q^{7} - 4 q^{11} + q^{13} - 3 q^{17} - q^{19} + O(q^{20})\) Copy content Toggle raw display