Properties

Label 257600cm
Number of curves $1$
Conductor $257600$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("cm1")
 
E.isogeny_class()
 

Elliptic curves in class 257600cm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
257600.cm1 257600cm1 \([0, 0, 0, 1472500, -164950000]\) \(137927116575/84410368\) \(-216090542080000000000\) \([]\) \(7004160\) \(2.5910\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 257600cm1 has rank \(0\).

Complex multiplication

The elliptic curves in class 257600cm do not have complex multiplication.

Modular form 257600.2.a.cm

sage: E.q_eigenform(10)
 
\(q - q^{7} - 3 q^{9} - 4 q^{11} + q^{13} - 3 q^{17} + 8 q^{19} + O(q^{20})\) Copy content Toggle raw display