Elliptic curve isogeny class with Cremona label 2275c (LMFDB label 2275.e)

• Label: 2275c
• Number of curves: $4$
• Conductor: $2275$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 2275c have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(5\)	\(1\)
\(7\)	\(1 - T\)
\(13\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 + T + 2 T^{2}\)	1.2.b
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 2275c do not have complex multiplication.

Modular form 2275.2.a.c

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 2275c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
2275.e3	2275c1	\([1, -1, 0, -1667, 26616]\)	\(32798729601/3185\)	\(49765625\)	\([2]\)	\(768\)	\(0.51270\)	\(\Gamma_0(N)\)-optimal
2275.e2	2275c2	\([1, -1, 0, -1792, 22491]\)	\(40743095121/10144225\)	\(158503515625\)	\([2, 2]\)	\(1536\)	\(0.85927\)
2275.e1	2275c3	\([1, -1, 0, -9917, -359384]\)	\(6903498885921/374712065\)	\(5854876015625\)	\([2]\)	\(3072\)	\(1.2058\)
2275.e4	2275c4	\([1, -1, 0, 4333, 138866]\)	\(575722725759/874680625\)	\(-13666884765625\)	\([2]\)	\(3072\)	\(1.2058\)