Properties

Label 805.c
Number of curves $1$
Conductor $805$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 805.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
805.c1 805a1 \([0, -1, 1, 23004, 2393001]\) \(1346216501445963776/3268768272021875\) \(-3268768272021875\) \([]\) \(5720\) \(1.6608\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 805.c1 has rank \(1\).

Complex multiplication

The elliptic curves in class 805.c do not have complex multiplication.

Modular form 805.2.a.c

sage: E.q_eigenform(10)
 
\(q + 2 q^{2} - q^{3} + 2 q^{4} - q^{5} - 2 q^{6} - q^{7} - 2 q^{9} - 2 q^{10} - 5 q^{11} - 2 q^{12} + 3 q^{13} - 2 q^{14} + q^{15} - 4 q^{16} - 5 q^{17} - 4 q^{18} + O(q^{20})\) Copy content Toggle raw display