Properties

Label 91728.cg
Number of curves $1$
Conductor $91728$
CM no
Rank $0$

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Show commands: SageMath
Copy content sage:E = EllipticCurve("cg1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 91728.cg1 has rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(3\)\(1\)
\(7\)\(1\)
\(13\)\(1 + T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(5\) \( 1 + T + 5 T^{2}\) 1.5.b
\(11\) \( 1 + T + 11 T^{2}\) 1.11.b
\(17\) \( 1 - 3 T + 17 T^{2}\) 1.17.ad
\(19\) \( 1 + T + 19 T^{2}\) 1.19.b
\(23\) \( 1 - 3 T + 23 T^{2}\) 1.23.ad
\(29\) \( 1 + 3 T + 29 T^{2}\) 1.29.d
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 91728.cg do not have complex multiplication.

Modular form 91728.2.a.cg

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

Elliptic curves in class 91728.cg

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
91728.cg1 91728b1 \([0, 0, 0, 416157, -128721726]\) \(1225217998314/1809323971\) \(-11770591658665641984\) \([]\) \(1290240\) \(2.3448\) \(\Gamma_0(N)\)-optimal