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Properties

Label 379050.jt
Number of curves $1$
Conductor $379050$
CM no
Rank $1$

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Show commands: SageMath
Copy content sage:E = EllipticCurve("jt1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 379050.jt1 has rank \(1\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1 - T\)
\(3\)\(1 - T\)
\(5\)\(1\)
\(7\)\(1 - T\)
\(19\)\(1\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(11\) \( 1 - 2 T + 11 T^{2}\) 1.11.ac
\(13\) \( 1 - T + 13 T^{2}\) 1.13.ab
\(17\) \( 1 - T + 17 T^{2}\) 1.17.ab
\(23\) \( 1 + 7 T + 23 T^{2}\) 1.23.h
\(29\) \( 1 + T + 29 T^{2}\) 1.29.b
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 379050.jt do not have complex multiplication.

Modular form 379050.2.a.jt

Copy content sage:E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{6} + q^{7} + q^{8} + q^{9} + 2 q^{11} + q^{12} + q^{13} + q^{14} + q^{16} + q^{17} + q^{18} + O(q^{20})\) Copy content Toggle raw display

Elliptic curves in class 379050.jt

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
379050.jt1 379050jt1 \([1, 0, 0, -11018, 529662]\) \(-125768785/30618\) \(-36011269611450\) \([]\) \(1161216\) \(1.3197\) \(\Gamma_0(N)\)-optimal