Elliptic curve isogeny class with Cremona label 194208m (LMFDB label 194208.cd)

• Label: 194208m
• Number of curves: $4$
• Conductor: $194208$
• CM: no
• Rank: $1$

Elliptic curves in class 194208m

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
194208.cd3	194208m1	\([0, 1, 0, -4142, 93240]\)	\(5088448/441\)	\(681258747456\)	\([2, 2]\)	\(327680\)	\(1.0114\)	\(\Gamma_0(N)\)-optimal
194208.cd1	194208m2	\([0, 1, 0, -64832, 6332172]\)	\(2438569736/21\)	\(259527141888\)	\([2]\)	\(655360\)	\(1.3580\)
194208.cd4	194208m3	\([0, 1, 0, 4528, 440040]\)	\(830584/7203\)	\(-89017809667584\)	\([2]\)	\(655360\)	\(1.3580\)
194208.cd2	194208m4	\([0, 1, 0, -14257, -552097]\)	\(3241792/567\)	\(56057862647808\)	\([2]\)	\(655360\)	\(1.3580\)

Rank

The elliptic curves in class 194208m have rank \(1\).

Complex multiplication

The elliptic curves in class 194208m do not have complex multiplication.

Modular form 194208.2.a.m

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.