Properties

Label 215475a
Number of curves $1$
Conductor $215475$
CM no
Rank $2$

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

Elliptic curves in class 215475a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
215475.g1 215475a1 \([0, 1, 1, -2105458, 2781846994]\) \(-49836032/132651\) \(-2747455949859029296875\) \([]\) \(17297280\) \(2.8012\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 215475a1 has rank \(2\).

Complex multiplication

The elliptic curves in class 215475a do not have complex multiplication.

Modular form 215475.2.a.a

sage: E.q_eigenform(10)
 
\(q - 2 q^{2} + q^{3} + 2 q^{4} - 2 q^{6} + q^{9} - 2 q^{11} + 2 q^{12} - 4 q^{16} - q^{17} - 2 q^{18} + 6 q^{19} + O(q^{20})\) Copy content Toggle raw display