Elliptic curve isogeny class with LMFDB label 333270.i (Cremona label 333270i)

• Label: 333270.i
• Number of curves: $4$
• Conductor: $333270$
• CM: no
• Rank: $1$

Elliptic curves in class 333270.i

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
333270.i1	333270i3	\([1, -1, 0, -174241590, 885313504376]\)	\(5421065386069310769/1919709260\)	\(207171496988785830060\)	\([2]\)	\(51904512\)	\(3.2528\)
333270.i2	333270i2	\([1, -1, 0, -10939290, 13703808356]\)	\(1341518286067569/24894528400\)	\(2686571775695786000400\)	\([2, 2]\)	\(25952256\)	\(2.9062\)
333270.i3	333270i1	\([1, -1, 0, -1417290, -325906444]\)	\(2917464019569/1262240000\)	\(136218622167361440000\)	\([2]\)	\(12976128\)	\(2.5596\)	\(\Gamma_0(N)\)-optimal
333270.i4	333270i4	\([1, -1, 0, 11010, 39881595536]\)	\(1367631/6366992112460\)	\(-687114093127898972089260\)	\([2]\)	\(51904512\)	\(3.2528\)

Rank

The elliptic curves in class 333270.i have rank \(1\).

Complex multiplication

The elliptic curves in class 333270.i do not have complex multiplication.

Modular form 333270.2.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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.