Properties

Label 73920fl
Number of curves $1$
Conductor $73920$
CM no
Rank $1$

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Show commands: SageMath
Copy content sage:E = EllipticCurve("fl1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 73920fl1 has rank \(1\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(3\)\(1 - T\)
\(5\)\(1 + T\)
\(7\)\(1 - T\)
\(11\)\(1 + T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(13\) \( 1 - 2 T + 13 T^{2}\) 1.13.ac
\(17\) \( 1 + 2 T + 17 T^{2}\) 1.17.c
\(19\) \( 1 + 4 T + 19 T^{2}\) 1.19.e
\(23\) \( 1 + 6 T + 23 T^{2}\) 1.23.g
\(29\) \( 1 - 10 T + 29 T^{2}\) 1.29.ak
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 73920fl do not have complex multiplication.

Modular form 73920.2.a.fl

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

Elliptic curves in class 73920fl

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
73920.cq1 73920fl1 \([0, -1, 0, 2555, -13475]\) \(112539892736/69328875\) \(-1135884288000\) \([]\) \(92160\) \(1.0023\) \(\Gamma_0(N)\)-optimal