Elliptic curve isogeny class with LMFDB label 139656.l (Cremona label 139656bf)

• Label: 139656.l
• Number of curves: $4$
• Conductor: $139656$
• CM: no
• Rank: $1$

Elliptic curves in class 139656.l

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
139656.l1	139656bf3	\([0, -1, 0, -21045912, 37168943868]\)	\(6800800113599908/27276183\)	\(4134762494906047488\)	\([4]\)	\(5406720\)	\(2.7835\)
139656.l2	139656bf4	\([0, -1, 0, -4012112, -2395804068]\)	\(47116822207108/10890820413\)	\(1650925856540469408768\)	\([2]\)	\(5406720\)	\(2.7835\)
139656.l3	139656bf2	\([0, -1, 0, -1335372, 562528980]\)	\(6949024664272/419963049\)	\(15915418446301583616\)	\([2, 2]\)	\(2703360\)	\(2.4369\)
139656.l4	139656bf1	\([0, -1, 0, 63833, 36427900]\)	\(12144109568/249338331\)	\(-590576343861780144\)	\([2]\)	\(1351680\)	\(2.0903\)	\(\Gamma_0(N)\)-optimal

Rank

The elliptic curves in class 139656.l have rank \(1\).

Complex multiplication

The elliptic curves in class 139656.l do not have complex multiplication.

Modular form 139656.2.a.l

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.