Elliptic curve isogeny class with LMFDB label 13680.e (Cremona label 13680bd)

• Label: 13680.e
• Number of curves: $4$
• Conductor: $13680$
• CM: no
• Rank: $1$

Elliptic curves in class 13680.e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
13680.e1	13680bd4	\([0, 0, 0, -70917123, 229866020098]\)	\(13209596798923694545921/92340\)	\(275725762560\)	\([2]\)	\(737280\)	\(2.7299\)
13680.e2	13680bd3	\([0, 0, 0, -4487043, 3498419842]\)	\(3345930611358906241/165622259047500\)	\(494545415559690240000\)	\([2]\)	\(737280\)	\(2.7299\)
13680.e3	13680bd2	\([0, 0, 0, -4432323, 3591651778]\)	\(3225005357698077121/8526675600\)	\(25460516914790400\)	\([2, 2]\)	\(368640\)	\(2.3834\)
13680.e4	13680bd1	\([0, 0, 0, -273603, 57571522]\)	\(-758575480593601/40535043840\)	\(-121036992345538560\)	\([2]\)	\(184320\)	\(2.0368\)	\(\Gamma_0(N)\)-optimal

Rank

The elliptic curves in class 13680.e have rank \(1\).

Complex multiplication

The elliptic curves in class 13680.e do not have complex multiplication.

Modular form 13680.2.a.e

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.