Properties

Label 8400bd
Number of curves $1$
Conductor $8400$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("bd1")
 
E.isogeny_class()
 

Elliptic curves in class 8400bd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8400.cc1 8400bd1 \([0, 1, 0, -708, -8037]\) \(-6288640/567\) \(-3543750000\) \([]\) \(3840\) \(0.57556\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 8400bd1 has rank \(1\).

Complex multiplication

The elliptic curves in class 8400bd do not have complex multiplication.

Modular form 8400.2.a.bd

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