Properties

Label 323680.bt
Number of curves $1$
Conductor $323680$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("bt1")
 
E.isogeny_class()
 

Elliptic curves in class 323680.bt

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
323680.bt1 323680bt1 \([0, 0, 0, 2312, 78608]\) \(13824/35\) \(-3460361891840\) \([]\) \(992256\) \(1.0898\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 323680.bt1 has rank \(1\).

Complex multiplication

The elliptic curves in class 323680.bt do not have complex multiplication.

Modular form 323680.2.a.bt

sage: E.q_eigenform(10)
 
\(q + 3 q^{3} - q^{5} + q^{7} + 6 q^{9} + 3 q^{11} + q^{13} - 3 q^{15} + 4 q^{19} + O(q^{20})\) Copy content Toggle raw display