Elliptic curve isogeny class with Cremona label 354025ce (LMFDB label 354025.ce)

• Label: 354025ce
• Number of curves: $2$
• Conductor: $354025$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 354025ce have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(5\)	\(1\)
\(7\)	\(1\)
\(17\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 - T + 2 T^{2}\)	1.2.ab
\(3\)	\( 1 + T + 3 T^{2}\)	1.3.b
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(19\)	\( 1 + 6 T + 19 T^{2}\)	1.19.g
\(23\)	\( 1 - 3 T + 23 T^{2}\)	1.23.ad
\(29\)	\( 1 + 7 T + 29 T^{2}\)	1.29.h
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 354025ce do not have complex multiplication.

Modular form 354025.2.a.ce

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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 37 \\ 37 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 354025ce

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
354025.ce2	354025ce1	\([1, 1, 0, -57950, 5822125]\)	\(-9317\)	\(-2310040783203125\)	\([]\)	\(1228800\)	\(1.6864\)	\(\Gamma_0(N)\)-optimal
354025.ce1	354025ce2	\([1, 1, 0, -1503399825, -22437371662250]\)	\(-162677523113838677\)	\(-2310040783203125\)	\([]\)	\(45465600\)	\(3.4918\)