Properties

Label 301665.bc
Number of curves $1$
Conductor $301665$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("bc1")
 
E.isogeny_class()
 

Elliptic curves in class 301665.bc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
301665.bc1 301665bc1 \([0, 1, 1, -257131, -50276144]\) \(-11125051061994029056/1195810546875\) \(-202091982421875\) \([]\) \(1751040\) \(1.7755\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 301665.bc1 has rank \(1\).

Complex multiplication

The elliptic curves in class 301665.bc do not have complex multiplication.

Modular form 301665.2.a.bc

sage: E.q_eigenform(10)
 
\(q + q^{3} - 2 q^{4} - q^{5} + q^{7} + q^{9} - q^{11} - 2 q^{12} - q^{15} + 4 q^{16} - q^{17} + 5 q^{19} + O(q^{20})\) Copy content Toggle raw display