Elliptic curve isogeny class with Cremona label 7514i (LMFDB label 7514.i)

• Label: 7514i
• Number of curves: $2$
• Conductor: $7514$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 7514i have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(13\)	\(1 + T\)
\(17\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - 3 T + 3 T^{2}\)	1.3.ad
\(5\)	\( 1 - T + 5 T^{2}\)	1.5.ab
\(7\)	\( 1 + T + 7 T^{2}\)	1.7.b
\(11\)	\( 1 - 2 T + 11 T^{2}\)	1.11.ac
\(19\)	\( 1 - 6 T + 19 T^{2}\)	1.19.ag
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 7514i do not have complex multiplication.

Modular form 7514.2.a.i

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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 7514i

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
7514.i2	7514i1	\([1, -1, 1, -777, 12937]\)	\(-2146689/1664\)	\(-40164914816\)	\([]\)	\(10080\)	\(0.73345\)	\(\Gamma_0(N)\)-optimal
7514.i1	7514i2	\([1, -1, 1, -61467, -6420203]\)	\(-1064019559329/125497034\)	\(-3029193317470346\)	\([]\)	\(70560\)	\(1.7064\)