Elliptic curve isogeny class with Cremona label 102960ew (LMFDB label 102960.ev)

• Label: 102960ew
• Number of curves: $4$
• Conductor: $102960$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 102960ew have rank \(0\).

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 \(\mathbb{F}_p\)
\(7\)	\( 1 - 5 T + 7 T^{2}\)	1.7.af
\(17\)	\( 1 - 3 T + 17 T^{2}\)	1.17.ad
\(19\)	\( 1 + 3 T + 19 T^{2}\)	1.19.d
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 - T + 29 T^{2}\)	1.29.ab
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 102960.2.a.ew

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 102960ew

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
102960.ev4	102960ew1	\([0, 0, 0, 14973, -14974]\)	\(124326214271/71980480\)	\(-214932561592320\)	\([2]\)	\(442368\)	\(1.4396\)	\(\Gamma_0(N)\)-optimal
102960.ev3	102960ew2	\([0, 0, 0, -59907, -119806]\)	\(7962857630209/4606058600\)	\(13753617282662400\)	\([2]\)	\(884736\)	\(1.7861\)
102960.ev2	102960ew3	\([0, 0, 0, -206787, -38645566]\)	\(-327495950129089/26547449500\)	\(-79270259447808000\)	\([2]\)	\(1327104\)	\(1.9889\)
102960.ev1	102960ew4	\([0, 0, 0, -3370467, -2381666974]\)	\(1418098748958579169/8307406250\)	\(24805782144000000\)	\([2]\)	\(2654208\)	\(2.3355\)