Properties

Label 32448m
Number of curves $1$
Conductor $32448$
CM no
Rank $1$

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

Elliptic curves in class 32448m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
32448.c1 32448m1 \([0, -1, 0, 1465, -53379]\) \(6656/27\) \(-1409582685888\) \([]\) \(74880\) \(1.0138\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 32448m1 has rank \(1\).

Complex multiplication

The elliptic curves in class 32448m do not have complex multiplication.

Modular form 32448.2.a.m

sage: E.q_eigenform(10)
 
\(q - q^{3} - 4 q^{5} + 3 q^{7} + q^{9} - 2 q^{11} + 4 q^{15} + 6 q^{17} + 4 q^{19} + O(q^{20})\) Copy content Toggle raw display