Properties

Label 8112.bb
Number of curves $1$
Conductor $8112$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("bb1")
 
E.isogeny_class()
 

Elliptic curves in class 8112.bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8112.bb1 8112bb1 \([0, 1, 0, -9520, 13720916]\) \(-169/144\) \(-81312247096344576\) \([]\) \(59904\) \(1.9238\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 8112.bb1 has rank \(1\).

Complex multiplication

The elliptic curves in class 8112.bb do not have complex multiplication.

Modular form 8112.2.a.bb

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