Properties

Label 392784cm
Number of curves $1$
Conductor $392784$
CM no
Rank $1$

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

Elliptic curves in class 392784cm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
392784.cm1 392784cm1 \([0, 1, 0, -2558600, 1576666356]\) \(-3843995587427449/6390046584\) \(-3079301490937921536\) \([]\) \(9144576\) \(2.4435\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 392784cm1 has rank \(1\).

Complex multiplication

The elliptic curves in class 392784cm do not have complex multiplication.

Modular form 392784.2.a.cm

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{5} + q^{9} - 2 q^{11} + 6 q^{13} + q^{15} + 4 q^{17} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display