Elliptic curve isogeny class with Cremona label 78033b (LMFDB label 78033.a)

• Label: 78033b
• Number of curves: $4$
• Conductor: $78033$
• CM: no
• Rank: $1$

Elliptic curves in class 78033b

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
78033.a3	78033b1	$[1, 0, 0, -2082, -31773]$	$389017/57$	$146246405313$	$[2]$	$72576$	$0.86730$	$\Gamma_0(N)$-optimal
78033.a2	78033b2	$[1, 0, 0, -8927, 292680]$	$30664297/3249$	$8336045102841$	$[2, 2]$	$145152$	$1.2139$
78033.a4	78033b3	$[1, 0, 0, 11608, 1446747]$	$67419143/390963$	$-1003104094041867$	$[2]$	$290304$	$1.5604$
78033.a1	78033b4	$[1, 0, 0, -138982, 19930985]$	$115714886617/1539$	$3948652943451$	$[2]$	$290304$	$1.5604$

Rank

The elliptic curves in class 78033b have rank $1$.

Complex multiplication

The elliptic curves in class 78033b do not have complex multiplication.

Modular form 78033.2.a.b

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.