Properties

Label 53312bm
Number of curves $1$
Conductor $53312$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("bm1")
 
E.isogeny_class()
 

Elliptic curves in class 53312bm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
53312.c1 53312bm1 \([0, 0, 0, -17836, -2266544]\) \(-1660932/4913\) \(-1856141217824768\) \([]\) \(516096\) \(1.6167\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 53312bm1 has rank \(0\).

Complex multiplication

The elliptic curves in class 53312bm do not have complex multiplication.

Modular form 53312.2.a.bm

sage: E.q_eigenform(10)
 
\(q - 3 q^{3} - 2 q^{5} + 6 q^{9} + 5 q^{11} + 7 q^{13} + 6 q^{15} - q^{17} + 2 q^{19} + O(q^{20})\) Copy content Toggle raw display