Properties

Label 35574.e
Number of curves $1$
Conductor $35574$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 35574.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
35574.e1 35574a1 \([1, 1, 0, -409763, -101133171]\) \(-991656390179/31104\) \(-238659440874624\) \([]\) \(282240\) \(1.8550\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 35574.e1 has rank \(1\).

Complex multiplication

The elliptic curves in class 35574.e do not have complex multiplication.

Modular form 35574.2.a.e

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} - q^{8} + q^{9} + q^{10} - q^{12} + 2 q^{13} + q^{15} + q^{16} - q^{17} - q^{18} - 6 q^{19} + O(q^{20})\) Copy content Toggle raw display