Elliptic curve isogeny class with LMFDB label 90.c (Cremona label 90c)

• Label: 90.c
• Number of curves: $8$
• Conductor: $90$
• CM: no
• Rank: $0$

Elliptic curves in class 90.c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
90.c1	90c8	$[1, -1, 1, -48002, 4059929]$	$16778985534208729/81000$	$59049000$	$[6]$	$192$	$1.1135$
90.c2	90c7	$[1, -1, 1, -4082, 14681]$	$10316097499609/5859375000$	$4271484375000$	$[6]$	$192$	$1.1135$
90.c3	90c6	$[1, -1, 1, -3002, 63929]$	$4102915888729/9000000$	$6561000000$	$[2, 6]$	$96$	$0.76690$
90.c4	90c4	$[1, -1, 1, -2597, -50281]$	$2656166199049/33750$	$24603750$	$[2]$	$64$	$0.56417$
90.c5	90c5	$[1, -1, 1, -617, 5231]$	$35578826569/5314410$	$3874204890$	$[2]$	$64$	$0.56417$
90.c6	90c2	$[1, -1, 1, -167, -709]$	$702595369/72900$	$53144100$	$[2, 2]$	$32$	$0.21759$
90.c7	90c3	$[1, -1, 1, -122, 1721]$	$-273359449/1536000$	$-1119744000$	$[12]$	$48$	$0.42032$
90.c8	90c1	$[1, -1, 1, 13, -61]$	$357911/2160$	$-1574640$	$[4]$	$16$	$-0.12898$	$\Gamma_0(N)$-optimal

Rank

The elliptic curves in class 90.c have rank $0$.

Complex multiplication

The elliptic curves in class 90.c do not have complex multiplication.

Modular form 90.2.a.c

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.