Properties

Label 381150.q
Number of curves $1$
Conductor $381150$
CM no
Rank $0$

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Show commands: SageMath
Copy content sage:E = EllipticCurve("q1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 381150.q1 has rank \(0\).

L-function data

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

Complex multiplication

The elliptic curves in class 381150.q do not have complex multiplication.

Modular form 381150.2.a.q

Copy content sage:E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{7} - q^{8} - 5 q^{13} + q^{14} + q^{16} - q^{19} + O(q^{20})\) Copy content Toggle raw display

Elliptic curves in class 381150.q

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
381150.q1 381150q1 \([1, -1, 0, -12197367, 40377608541]\) \(-3287705905/9633792\) \(-588066323573836800000000\) \([]\) \(48660480\) \(3.2479\) \(\Gamma_0(N)\)-optimal