Properties

Label 816.i
Number of curves $1$
Conductor $816$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 816.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
816.i1 816i1 \([0, 1, 0, -1621, 24623]\) \(-1841198792704/3011499\) \(-770943744\) \([]\) \(528\) \(0.60190\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 816.i1 has rank \(1\).

Complex multiplication

The elliptic curves in class 816.i do not have complex multiplication.

Modular form 816.2.a.i

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{5} - 4 q^{7} + q^{9} - 3 q^{11} + 3 q^{13} - q^{15} - q^{17} - q^{19} + O(q^{20})\) Copy content Toggle raw display