Elliptic curve isogeny class with Cremona label 18496i (LMFDB label 18496.j)

• Label: 18496i
• Number of curves: $4$
• Conductor: $18496$
• CM: \(\Q(\sqrt{-1}) \)
• Rank: $2$

Rank

The elliptic curves in class 18496i have rank \(2\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 4 T + 23 T^{2}\)	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

Each elliptic curve in class 18496i has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-1}) \).

Modular form 18496.2.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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 18496i

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
18496.j4	18496i1	\([0, 0, 0, 289, 0]\)	\(1728\)	\(-1544804416\)	\([2]\)	\(5120\)	\(0.45265\)	\(\Gamma_0(N)\)-optimal	\(-4\)
18496.j3	18496i2	\([0, 0, 0, -1156, 0]\)	\(1728\)	\(98867482624\)	\([2, 2]\)	\(10240\)	\(0.79922\)		\(-4\)
18496.j1	18496i3	\([0, 0, 0, -12716, -550256]\)	\(287496\)	\(790939860992\)	\([2]\)	\(20480\)	\(1.1458\)		\(-16\)
18496.j2	18496i4	\([0, 0, 0, -12716, 550256]\)	\(287496\)	\(790939860992\)	\([2]\)	\(20480\)	\(1.1458\)		\(-16\)