Properties

Label 1323.e
Number of curves $1$
Conductor $1323$
CM no
Rank $1$

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

Elliptic curves in class 1323.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1323.e1 1323p1 \([1, -1, 1, 1, 4]\) \(27\) \(-9261\) \([]\) \(96\) \(-0.55897\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1323.e1 has rank \(1\).

Complex multiplication

The elliptic curves in class 1323.e do not have complex multiplication.

Modular form 1323.2.a.e

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{4} - 3 q^{5} + 3 q^{8} + 3 q^{10} + 5 q^{11} - 6 q^{13} - q^{16} + 6 q^{17} - 3 q^{19} + O(q^{20})\) Copy content Toggle raw display