Properties

Label 212415bt
Number of curves $1$
Conductor $212415$
CM no
Rank $1$

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

Elliptic curves in class 212415bt

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
212415.cn1 212415bt1 \([1, 0, 1, -8138079178, 282572611137401]\) \(-72628961394279272329/24608375505\) \(-20195869525163740174360545\) \([]\) \(163918080\) \(4.2127\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 212415bt1 has rank \(1\).

Complex multiplication

The elliptic curves in class 212415bt do not have complex multiplication.

Modular form 212415.2.a.bt

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} - q^{4} + q^{5} + q^{6} - 3 q^{8} + q^{9} + q^{10} - q^{11} - q^{12} + q^{13} + q^{15} - q^{16} + q^{18} + O(q^{20})\) Copy content Toggle raw display