Properties

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

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Show commands: SageMath
E = EllipticCurve("bj1")
 
E.isogeny_class()
 

Elliptic curves in class 53312bj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
53312.x1 53312bj1 \([0, -1, 0, -14177, 817153]\) \(-208537/68\) \(-102762143547392\) \([]\) \(129024\) \(1.4011\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 53312bj1 has rank \(0\).

Complex multiplication

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

Modular form 53312.2.a.bj

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