Elliptic curve isogeny class with LMFDB label 5415.j (Cremona label 5415k)

• Label: 5415.j
• Number of curves: $8$
• Conductor: $5415$
• CM: no
• Rank: $0$

Elliptic curves in class 5415.j

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
5415.j1	5415k7	\([1, 0, 1, -779768, 264965501]\)	\(1114544804970241/405\)	\(19053581805\)	\([2]\)	\(27648\)	\(1.7631\)
5415.j2	5415k5	\([1, 0, 1, -48743, 4135781]\)	\(272223782641/164025\)	\(7716700631025\)	\([2, 2]\)	\(13824\)	\(1.4165\)
5415.j3	5415k8	\([1, 0, 1, -39718, 5716961]\)	\(-147281603041/215233605\)	\(-10125854568031005\)	\([2]\)	\(27648\)	\(1.7631\)
5415.j4	5415k3	\([1, 0, 1, -28888, -1892197]\)	\(56667352321/15\)	\(705688215\)	\([2]\)	\(6912\)	\(1.0699\)
5415.j5	5415k4	\([1, 0, 1, -3618, 38431]\)	\(111284641/50625\)	\(2381697725625\)	\([2, 2]\)	\(6912\)	\(1.0699\)
5415.j6	5415k2	\([1, 0, 1, -1813, -29437]\)	\(13997521/225\)	\(10585323225\)	\([2, 2]\)	\(3456\)	\(0.72337\)
5415.j7	5415k1	\([1, 0, 1, -8, -1279]\)	\(-1/15\)	\(-705688215\)	\([2]\)	\(1728\)	\(0.37679\)	\(\Gamma_0(N)\)-optimal
5415.j8	5415k6	\([1, 0, 1, 12627, 291853]\)	\(4733169839/3515625\)	\(-165395675390625\)	\([2]\)	\(13824\)	\(1.4165\)

Rank

The elliptic curves in class 5415.j have rank \(0\).

Complex multiplication

The elliptic curves in class 5415.j do not have complex multiplication.

Modular form 5415.2.a.j

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.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 16 & 4 & 8 & 16 & 8 \\ 2 & 1 & 2 & 8 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 16 & 4 & 8 & 16 & 8 \\ 16 & 8 & 16 & 1 & 4 & 2 & 4 & 8 \\ 4 & 2 & 4 & 4 & 1 & 2 & 4 & 2 \\ 8 & 4 & 8 & 2 & 2 & 1 & 2 & 4 \\ 16 & 8 & 16 & 4 & 4 & 2 & 1 & 8 \\ 8 & 4 & 8 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.