Elliptic curve isogeny class with Cremona label 45968u (LMFDB label 45968.c)

• Label: 45968u
• Number of curves: $2$
• Conductor: $45968$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 45968u have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - 2 T + 3 T^{2}\)	1.3.ac
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(11\)	\( 1 + 6 T + 11 T^{2}\)	1.11.g
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 + 10 T + 29 T^{2}\)	1.29.k
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 45968u do not have complex multiplication.

Modular form 45968.2.a.u

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 45968u

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
45968.c1	45968u1	\([0, 1, 0, -147424, 20951412]\)	\(17923019113/735488\)	\(14541046160556032\)	\([2]\)	\(258048\)	\(1.8668\)	\(\Gamma_0(N)\)-optimal
45968.c2	45968u2	\([0, 1, 0, 68896, 77454196]\)	\(1829276567/132066064\)	\(-2611026601204842496\)	\([2]\)	\(516096\)	\(2.2134\)