Elliptic curve isogeny class with LMFDB label 272.b (Cremona label 272b)

• Label: 272.b
• Number of curves: $4$
• Conductor: $272$
• CM: no
• Rank: $1$

Elliptic curves in class 272.b

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
272.b1	272b3	$[0, 0, 0, -1451, 21274]$	$82483294977/17$	$69632$	$[4]$	$64$	$0.31651$
272.b2	272b2	$[0, 0, 0, -91, 330]$	$20346417/289$	$1183744$	$[2, 2]$	$32$	$-0.030063$
272.b3	272b1	$[0, 0, 0, -11, -6]$	$35937/17$	$69632$	$[2]$	$16$	$-0.37664$	$\Gamma_0(N)$-optimal
272.b4	272b4	$[0, 0, 0, -11, 890]$	$-35937/83521$	$-342102016$	$[4]$	$64$	$0.31651$

Rank

The elliptic curves in class 272.b have rank $1$.

Complex multiplication

The elliptic curves in class 272.b do not have complex multiplication.

Modular form 272.2.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 LMFDB 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 LMFDB labels.