Properties

Label 215.a
Number of curves $1$
Conductor $215$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 215.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
215.a1 215a1 \([0, 0, 1, -8, -12]\) \(-56623104/26875\) \(-26875\) \([]\) \(8\) \(-0.44421\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 215.a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 215.a do not have complex multiplication.

Modular form 215.2.a.a

sage: E.q_eigenform(10)
 
\(q - 2 q^{4} - q^{5} - 2 q^{7} - 3 q^{9} - q^{11} - q^{13} + 4 q^{16} - 3 q^{17} - 2 q^{19} + O(q^{20})\) Copy content Toggle raw display