Elliptic curve isogeny class with LMFDB label 102960.co (Cremona label 102960eh)

• Label: 102960.co
• Number of curves: $4$
• Conductor: $102960$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 102960.co have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1 - T\)
\(11\)	\(1 + T\)
\(13\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 102960.co do not have complex multiplication.

Modular form 102960.2.a.co

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 LMFDB numbering.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 102960.co

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
102960.co1	102960eh4	\([0, 0, 0, -5493387, -4955736134]\)	\(6139836723518159689/3799803150\)	\(11346151409049600\)	\([2]\)	\(2359296\)	\(2.4016\)
102960.co2	102960eh3	\([0, 0, 0, -773067, 150465274]\)	\(17111482619973769/6627044531250\)	\(19788248937600000000\)	\([4]\)	\(2359296\)	\(2.4016\)
102960.co3	102960eh2	\([0, 0, 0, -345387, -76461734]\)	\(1525998818291689/37268302500\)	\(111282554972160000\)	\([2, 2]\)	\(1179648\)	\(2.0550\)
102960.co4	102960eh1	\([0, 0, 0, 3093, -3768806]\)	\(1095912791/2055596400\)	\(-6137977960857600\)	\([2]\)	\(589824\)	\(1.7084\)	\(\Gamma_0(N)\)-optimal