Properties

Label 819.e
Number of curves $1$
Conductor $819$
CM no
Rank $0$

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

Elliptic curves in class 819.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
819.e1 819f1 \([0, 0, 1, -237, -1607]\) \(-2019487744/361179\) \(-263299491\) \([]\) \(384\) \(0.34109\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 819.e1 has rank \(0\).

Complex multiplication

The elliptic curves in class 819.e do not have complex multiplication.

Modular form 819.2.a.e

sage: E.q_eigenform(10)
 
\(q + 2 q^{2} + 2 q^{4} + q^{5} + q^{7} + 2 q^{10} + 2 q^{11} + q^{13} + 2 q^{14} - 4 q^{16} + 4 q^{17} + 3 q^{19} + O(q^{20})\) Copy content Toggle raw display