Elliptic curve isogeny class with Cremona label 15456r (LMFDB label 15456.l)

• Label: 15456r
• Number of curves: $4$
• Conductor: $15456$
• CM: no
• Rank: $1$

Elliptic curves in class 15456r

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
15456.l3	15456r1	\([0, 1, 0, -8694, 309096]\)	\(1135671162482368/170067681\)	\(10884331584\)	\([2, 2]\)	\(18432\)	\(0.93918\)	\(\Gamma_0(N)\)-optimal
15456.l2	15456r2	\([0, 1, 0, -9504, 247212]\)	\(185446537613576/54423757521\)	\(27864963850752\)	\([2]\)	\(36864\)	\(1.2858\)
15456.l1	15456r3	\([0, 1, 0, -139104, 19922760]\)	\(581400938887066376/13041\)	\(6676992\)	\([2]\)	\(36864\)	\(1.2858\)
15456.l4	15456r4	\([0, 1, 0, -7889, 369471]\)	\(-13258203533632/6930522081\)	\(-28387418443776\)	\([4]\)	\(36864\)	\(1.2858\)

Rank

The elliptic curves in class 15456r have rank \(1\).

Complex multiplication

The elliptic curves in class 15456r do not have complex multiplication.

Modular form 15456.2.a.r

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.