Elliptic curve isogeny class with Cremona label 75c (LMFDB label 75.a)

• Label: 75c
• Number of curves: $2$
• Conductor: $75$
• CM: no
• Rank: $0$

Elliptic curves in class 75c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
75.a2	75c1	$[0, 1, 1, 2, 4]$	$20480/243$	$-6075$	$[5]$	$6$	$-0.59310$	$\Gamma_0(N)$-optimal
75.a1	75c2	$[0, 1, 1, -208, -1256]$	$-102400/3$	$-29296875$	$[]$	$30$	$0.21162$

Rank

The elliptic curves in class 75c have rank $0$.

Complex multiplication

The elliptic curves in class 75c do not have complex multiplication.

Modular form 75.2.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 Cremona numbering.

$\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with Cremona labels.