Elliptic curve isogeny class with Cremona label 92480eb (LMFDB label 92480.dy)

• Label: 92480eb
• Number of curves: $2$
• Conductor: $92480$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 92480eb have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1 - T\)
\(17\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - 2 T + 3 T^{2}\)	1.3.ac
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(11\)	\( 1 - 3 T + 11 T^{2}\)	1.11.ad
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(19\)	\( 1 + 5 T + 19 T^{2}\)	1.19.f
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 + 5 T + 29 T^{2}\)	1.29.f
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 92480eb do not have complex multiplication.

Modular form 92480.2.a.eb

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 92480eb

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
92480.dy1	92480eb1	\([0, -1, 0, -139105, -17250303]\)	\(47045881/6800\)	\(43027128437964800\)	\([2]\)	\(884736\)	\(1.9170\)	\(\Gamma_0(N)\)-optimal
92480.dy2	92480eb2	\([0, -1, 0, 230815, -93675775]\)	\(214921799/722500\)	\(-4571632396533760000\)	\([2]\)	\(1769472\)	\(2.2636\)