Properties

Label 3648.m
Number of curves $1$
Conductor $3648$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("m1")
 
E.isogeny_class()
 

Elliptic curves in class 3648.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3648.m1 3648z1 \([0, -1, 0, 5, 13]\) \(175616/1539\) \(-98496\) \([]\) \(256\) \(-0.36055\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 3648.m1 has rank \(1\).

Complex multiplication

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

Modular form 3648.2.a.m

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