Properties

Label 3648c
Number of curves $1$
Conductor $3648$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 3648c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3648.l1 3648c1 \([0, -1, 0, -375, 3933]\) \(-91368216064/45001899\) \(-2880121536\) \([]\) \(1536\) \(0.52037\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 3648c1 has rank \(1\).

Complex multiplication

The elliptic curves in class 3648c do not have complex multiplication.

Modular form 3648.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} - q^{7} + q^{9} + 5 q^{11} - 4 q^{13} - q^{15} - 3 q^{17} - q^{19} + O(q^{20})\) Copy content Toggle raw display