Elliptic curve isogeny class with LMFDB label 7335.c (Cremona label 7335c)

• Label: 7335.c
• Number of curves: $4$
• Conductor: $7335$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 7335.c have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1\)
\(5\)	\(1 - T\)
\(163\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 + T + 2 T^{2}\)	1.2.b
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 + 10 T + 29 T^{2}\)	1.29.k
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 7335.c do not have complex multiplication.

Modular form 7335.2.a.c

Isogeny matrix

The \((i,j)\)-th entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB 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 LMFDB labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 7335.c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
7335.c1	7335c3	\([1, -1, 1, -63302, -5995114]\)	\(38480618749557529/857682789615\)	\(625250753629335\)	\([2]\)	\(30720\)	\(1.6266\)
7335.c2	7335c2	\([1, -1, 1, -8627, 172226]\)	\(97393143178729/39221822025\)	\(28592708256225\)	\([2, 2]\)	\(15360\)	\(1.2800\)
7335.c3	7335c1	\([1, -1, 1, -7502, 251876]\)	\(64043209720729/24755625\)	\(18046850625\)	\([4]\)	\(7680\)	\(0.93340\)	\(\Gamma_0(N)\)-optimal
7335.c4	7335c4	\([1, -1, 1, 28048, 1228466]\)	\(3347467708032071/2841729286815\)	\(-2071620650088135\)	\([2]\)	\(30720\)	\(1.6266\)