Elliptic curve isogeny class with LMFDB label 17325.bl (Cremona label 17325x)

• Label: 17325.bl
• Number of curves: $2$
• Conductor: $17325$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 17325.bl have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1\)
\(5\)	\(1\)
\(7\)	\(1 - T\)
\(11\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 - T + 2 T^{2}\)	1.2.ab
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(17\)	\( 1 - 4 T + 17 T^{2}\)	1.17.ae
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 17325.bl do not have complex multiplication.

Modular form 17325.2.a.bl

Isogeny matrix

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 17325.bl

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
17325.bl1	17325x2	\([1, -1, 0, -11592, -440559]\)	\(15124197817/1294139\)	\(14741052046875\)	\([2]\)	\(36864\)	\(1.2680\)
17325.bl2	17325x1	\([1, -1, 0, 783, -32184]\)	\(4657463/41503\)	\(-472745109375\)	\([2]\)	\(18432\)	\(0.92143\)	\(\Gamma_0(N)\)-optimal