Properties

Label 37440cm
Number of curves $1$
Conductor $37440$
CM no
Rank $1$

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

Elliptic curves in class 37440cm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
37440.cy1 37440cm1 \([0, 0, 0, -12432, 533536]\) \(-17790954496/195\) \(-2329067520\) \([]\) \(61440\) \(0.95163\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 37440cm1 has rank \(1\).

Complex multiplication

The elliptic curves in class 37440cm do not have complex multiplication.

Modular form 37440.2.a.cm

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