Elliptic curve isogeny class with LMFDB label 76230.i (Cremona label 76230s)

• Label: 76230.i
• Number of curves: $8$
• Conductor: $76230$
• CM: no
• Rank: $1$

Elliptic curves in class 76230.i

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
76230.i1	76230s8	\([1, -1, 0, -279249570, 1685267693676]\)	\(1864737106103260904761/129177711985836360\)	\(166828877338415040615552840\)	\([2]\)	\(26542080\)	\(3.7795\)
76230.i2	76230s5	\([1, -1, 0, -274430745, 1749904259571]\)	\(1769857772964702379561/691787250\)	\(893421074737595250\)	\([2]\)	\(8847360\)	\(3.2302\)
76230.i3	76230s6	\([1, -1, 0, -55133370, -125904965004]\)	\(14351050585434661561/3001282273281600\)	\(3876059921870690917070400\)	\([2, 2]\)	\(13271040\)	\(3.4330\)
76230.i4	76230s3	\([1, -1, 0, -51997050, -144295718220]\)	\(12038605770121350841/757333463040\)	\(978071909368005365760\)	\([2]\)	\(6635520\)	\(3.0864\)
76230.i5	76230s2	\([1, -1, 0, -17154495, 27336855321]\)	\(432288716775559561/270140062500\)	\(348877237862408062500\)	\([2, 2]\)	\(4423680\)	\(2.8837\)
76230.i6	76230s4	\([1, -1, 0, -13920165, 37957748175]\)	\(-230979395175477481/348191894531250\)	\(-449678678852535644531250\)	\([2]\)	\(8847360\)	\(3.2302\)
76230.i7	76230s1	\([1, -1, 0, -1276875, 252811125]\)	\(178272935636041/81841914000\)	\(105696210452652666000\)	\([2]\)	\(2211840\)	\(2.5371\)	\(\Gamma_0(N)\)-optimal
76230.i8	76230s7	\([1, -1, 0, 118801710, -760107053700]\)	\(143584693754978072519/276341298967965000\)	\(-356885936128979554613085000\)	\([2]\)	\(26542080\)	\(3.7795\)

Rank

The elliptic curves in class 76230.i have rank \(1\).

Complex multiplication

The elliptic curves in class 76230.i do not have complex multiplication.

Modular form 76230.2.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.

\(\left(\begin{array}{rrrrrrrr} 1 & 3 & 2 & 4 & 6 & 12 & 12 & 4 \\ 3 & 1 & 6 & 12 & 2 & 4 & 4 & 12 \\ 2 & 6 & 1 & 2 & 3 & 6 & 6 & 2 \\ 4 & 12 & 2 & 1 & 6 & 12 & 3 & 4 \\ 6 & 2 & 3 & 6 & 1 & 2 & 2 & 6 \\ 12 & 4 & 6 & 12 & 2 & 1 & 4 & 3 \\ 12 & 4 & 6 & 3 & 2 & 4 & 1 & 12 \\ 4 & 12 & 2 & 4 & 6 & 3 & 12 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.