Elliptic curve isogeny class with Cremona label 14415g (LMFDB label 14415.d)

• Label: 14415g
• Number of curves: $8$
• Conductor: $14415$
• CM: no
• Rank: $0$

Elliptic curves in class 14415g

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
14415.d7	14415g1	\([1, 0, 0, -20, -5553]\)	\(-1/15\)	\(-13312555215\)	\([2]\)	\(7680\)	\(0.62157\)	\(\Gamma_0(N)\)-optimal
14415.d6	14415g2	\([1, 0, 0, -4825, -127600]\)	\(13997521/225\)	\(199688328225\)	\([2, 2]\)	\(15360\)	\(0.96814\)
14415.d4	14415g3	\([1, 0, 0, -76900, -8214415]\)	\(56667352321/15\)	\(13312555215\)	\([2]\)	\(30720\)	\(1.3147\)
14415.d5	14415g4	\([1, 0, 0, -9630, 167427]\)	\(111284641/50625\)	\(44929873850625\)	\([2, 2]\)	\(30720\)	\(1.3147\)
14415.d2	14415g5	\([1, 0, 0, -129755, 17969952]\)	\(272223782641/164025\)	\(145572791276025\)	\([2, 2]\)	\(61440\)	\(1.6613\)
14415.d8	14415g6	\([1, 0, 0, 33615, 1265850]\)	\(4733169839/3515625\)	\(-3120130128515625\)	\([2]\)	\(61440\)	\(1.6613\)
14415.d1	14415g7	\([1, 0, 0, -2075780, 1150945707]\)	\(1114544804970241/405\)	\(359438990805\)	\([2]\)	\(122880\)	\(2.0079\)
14415.d3	14415g8	\([1, 0, 0, -105730, 24836297]\)	\(-147281603041/215233605\)	\(-191020616712400005\)	\([2]\)	\(122880\)	\(2.0079\)

Rank

The elliptic curves in class 14415g have rank \(0\).

Complex multiplication

The elliptic curves in class 14415g do not have complex multiplication.

Modular form 14415.2.a.g

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.