Elliptic curve isogeny class with Cremona label 370881i (LMFDB label 370881.i)

• Label: 370881i
• Number of curves: $6$
• Conductor: $370881$
• CM: no
• Rank: $1$

Elliptic curves in class 370881i

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
370881.i5	370881i1	\([1, -1, 1, -290778431, 2043453982182]\)	\(-53297461115137/4513839183\)	\(-230276615606154943330533903\)	\([2]\)	\(123863040\)	\(3.8034\)	\(\Gamma_0(N)\)-optimal
370881.i4	370881i2	\([1, -1, 1, -4743204836, 125735421454206]\)	\(231331938231569617/1472026689\)	\(75096455651653194763768449\)	\([2, 2]\)	\(247726080\)	\(4.1500\)
370881.i1	370881i3	\([1, -1, 1, -75891161471, 8047035862185912]\)	\(947531277805646290177/38367\)	\(1957318936889858335647\)	\([2]\)	\(495452160\)	\(4.4966\)
370881.i3	370881i4	\([1, -1, 1, -4834070681, 120667469815176]\)	\(244883173420511137/18418027974129\)	\(939608385694212357643347645489\)	\([2, 2]\)	\(495452160\)	\(4.4966\)
370881.i6	370881i5	\([1, -1, 1, 4628958034, 535503937411860]\)	\(215015459663151503/2552757445339983\)	\(-130230679726080386150567228306703\)	\([2]\)	\(990904320\)	\(4.8431\)
370881.i2	370881i6	\([1, -1, 1, -15750952916, -618518993069568]\)	\(8471112631466271697/1662662681263647\)	\(84821882130409021497934145756127\)	\([2]\)	\(990904320\)	\(4.8431\)

Rank

The elliptic curves in class 370881i have rank \(1\).

Complex multiplication

The elliptic curves in class 370881i do not have complex multiplication.

Modular form 370881.2.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 Cremona numbering.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.