Properties

Label 369600.t
Number of curves $1$
Conductor $369600$
CM no
Rank $0$

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Show commands: SageMath
Copy content sage:E = EllipticCurve("t1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 369600.t1 has rank \(0\).

L-function data

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

Complex multiplication

The elliptic curves in class 369600.t do not have complex multiplication.

Modular form 369600.2.a.t

Copy content sage:E.q_eigenform(10)
 
\(q - q^{3} - q^{7} + q^{9} - q^{11} - 4 q^{13} - 4 q^{17} - 2 q^{19} + O(q^{20})\) Copy content Toggle raw display

Elliptic curves in class 369600.t

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
369600.t1 369600t1 \([0, -1, 0, -833, 3309537]\) \(-25/1848\) \(-4730880000000000\) \([]\) \(1935360\) \(1.6866\) \(\Gamma_0(N)\)-optimal