Elliptic curve isogeny class with LMFDB label 212940.i (Cremona label 212940bh)

• Label: 212940.i
• Number of curves: $4$
• Conductor: $212940$
• CM: no
• Rank: $1$

Elliptic curves in class 212940.i

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
212940.i1	212940bh4	\([0, 0, 0, -100988823, 286573881022]\)	\(126449185587012304/33791748046875\)	\(30439552668985687500000000\)	\([2]\)	\(41803776\)	\(3.5981\)
212940.i2	212940bh2	\([0, 0, 0, -35829183, -82521749882]\)	\(5646857395652944/2031631875\)	\(1830090748110075360000\)	\([2]\)	\(13934592\)	\(3.0488\)
212940.i3	212940bh1	\([0, 0, 0, -1918488, -1671870863]\)	\(-13870539341824/13420809675\)	\(-755590244983595002800\)	\([2]\)	\(6967296\)	\(2.7023\)	\(\Gamma_0(N)\)-optimal
212940.i4	212940bh3	\([0, 0, 0, 15968472, 29010525973]\)	\(7998456195055616/11086576921875\)	\(-624173173995107850750000\)	\([2]\)	\(20901888\)	\(3.2516\)

Rank

The elliptic curves in class 212940.i have rank \(1\).

Complex multiplication

The elliptic curves in class 212940.i do not have complex multiplication.

Modular form 212940.2.a.i

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.