Properties

Label 348480.ji
Number of curves $1$
Conductor $348480$
CM no
Rank $0$

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Show commands: SageMath
Copy content sage:E = EllipticCurve("ji1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 348480.ji1 has rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(3\)\(1\)
\(5\)\(1 - T\)
\(11\)\(1\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(7\) \( 1 + 4 T + 7 T^{2}\) 1.7.e
\(13\) \( 1 + 2 T + 13 T^{2}\) 1.13.c
\(17\) \( 1 + 3 T + 17 T^{2}\) 1.17.d
\(19\) \( 1 - 8 T + 19 T^{2}\) 1.19.ai
\(23\) \( 1 + T + 23 T^{2}\) 1.23.b
\(29\) \( 1 - 2 T + 29 T^{2}\) 1.29.ac
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 348480.ji do not have complex multiplication.

Modular form 348480.2.a.ji

Copy content sage:E.q_eigenform(10)
 
\(q + q^{5} - 4 q^{7} - 2 q^{13} - 3 q^{17} + 8 q^{19} + O(q^{20})\) Copy content Toggle raw display

Elliptic curves in class 348480.ji

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
348480.ji1 348480ji1 \([0, 0, 0, 2786388, 2950253944]\) \(218902267299584/470715894135\) \(-5144664857596170255360\) \([]\) \(19783680\) \(2.8503\) \(\Gamma_0(N)\)-optimal