Elliptic curve isogeny class with Cremona label 240d (LMFDB label 240.d)

• Label: 240d
• Number of curves: $8$
• Conductor: $240$
• CM: no
• Rank: $0$

Elliptic curves in class 240d

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
240.d7	240d1	\([0, 1, 0, 0, -12]\)	\(-1/15\)	\(-61440\)	\([2]\)	\(16\)	\(-0.40228\)	\(\Gamma_0(N)\)-optimal
240.d6	240d2	\([0, 1, 0, -80, -300]\)	\(13997521/225\)	\(921600\)	\([2, 2]\)	\(32\)	\(-0.055704\)
240.d4	240d3	\([0, 1, 0, -1280, -18060]\)	\(56667352321/15\)	\(61440\)	\([2]\)	\(64\)	\(0.29087\)
240.d5	240d4	\([0, 1, 0, -160, 308]\)	\(111284641/50625\)	\(207360000\)	\([2, 4]\)	\(64\)	\(0.29087\)
240.d2	240d5	\([0, 1, 0, -2160, 37908]\)	\(272223782641/164025\)	\(671846400\)	\([2, 4]\)	\(128\)	\(0.63744\)
240.d8	240d6	\([0, 1, 0, 560, 2900]\)	\(4733169839/3515625\)	\(-14400000000\)	\([4]\)	\(128\)	\(0.63744\)
240.d1	240d7	\([0, 1, 0, -34560, 2461428]\)	\(1114544804970241/405\)	\(1658880\)	\([4]\)	\(256\)	\(0.98402\)
240.d3	240d8	\([0, 1, 0, -1760, 52788]\)	\(-147281603041/215233605\)	\(-881596846080\)	\([4]\)	\(256\)	\(0.98402\)

Rank

The elliptic curves in class 240d have rank \(0\).

Complex multiplication

The elliptic curves in class 240d do not have complex multiplication.

Modular form 240.2.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.

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

Isogeny graph

The vertices are labelled with Cremona labels.