Elliptic curve isogeny class with Cremona label 1470d (LMFDB label 1470.d)

• Label: 1470d
• Number of curves: $8$
• Conductor: $1470$
• CM: no
• Rank: $1$

Elliptic curves in class 1470d

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
1470.d8	1470d1	\([1, 1, 0, 73, -699]\)	\(357911/2160\)	\(-254121840\)	\([2]\)	\(576\)	\(0.29467\)	\(\Gamma_0(N)\)-optimal
1470.d6	1470d2	\([1, 1, 0, -907, -9911]\)	\(702595369/72900\)	\(8576612100\)	\([2, 2]\)	\(1152\)	\(0.64124\)
1470.d7	1470d3	\([1, 1, 0, -662, 21204]\)	\(-273359449/1536000\)	\(-180708864000\)	\([2]\)	\(1728\)	\(0.84397\)
1470.d4	1470d4	\([1, 1, 0, -14137, -652889]\)	\(2656166199049/33750\)	\(3970653750\)	\([2]\)	\(2304\)	\(0.98781\)
1470.d5	1470d5	\([1, 1, 0, -3357, 63099]\)	\(35578826569/5314410\)	\(625235022090\)	\([2]\)	\(2304\)	\(0.98781\)
1470.d3	1470d6	\([1, 1, 0, -16342, 795796]\)	\(4102915888729/9000000\)	\(1058841000000\)	\([2, 2]\)	\(3456\)	\(1.1905\)
1470.d2	1470d7	\([1, 1, 0, -22222, 164284]\)	\(10316097499609/5859375000\)	\(689349609375000\)	\([2]\)	\(6912\)	\(1.5371\)
1470.d1	1470d8	\([1, 1, 0, -261342, 51314796]\)	\(16778985534208729/81000\)	\(9529569000\)	\([2]\)	\(6912\)	\(1.5371\)

Rank

The elliptic curves in class 1470d have rank \(1\).

Complex multiplication

The elliptic curves in class 1470d do not have complex multiplication.

Modular form 1470.2.a.d

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.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 3 & 4 & 4 & 6 & 12 & 12 \\ 2 & 1 & 6 & 2 & 2 & 3 & 6 & 6 \\ 3 & 6 & 1 & 12 & 12 & 2 & 4 & 4 \\ 4 & 2 & 12 & 1 & 4 & 6 & 3 & 12 \\ 4 & 2 & 12 & 4 & 1 & 6 & 12 & 3 \\ 6 & 3 & 2 & 6 & 6 & 1 & 2 & 2 \\ 12 & 6 & 4 & 3 & 12 & 2 & 1 & 4 \\ 12 & 6 & 4 & 12 & 3 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.