Elliptic curve isogeny class with LMFDB label 1815.d (Cremona label 1815a)

• Label: 1815.d
• Number of curves: $8$
• Conductor: $1815$
• CM: no
• Rank: $1$

Elliptic curves in class 1815.d

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
1815.d1	1815a7	\([1, 1, 0, -261362, 51320691]\)	\(1114544804970241/405\)	\(717482205\)	\([2]\)	\(5120\)	\(1.4898\)
1815.d2	1815a5	\([1, 1, 0, -16337, 796536]\)	\(272223782641/164025\)	\(290580293025\)	\([2, 2]\)	\(2560\)	\(1.1432\)
1815.d3	1815a8	\([1, 1, 0, -13312, 1104481]\)	\(-147281603041/215233605\)	\(-381299460507405\)	\([2]\)	\(5120\)	\(1.4898\)
1815.d4	1815a3	\([1, 1, 0, -9682, -370751]\)	\(56667352321/15\)	\(26573415\)	\([2]\)	\(1280\)	\(0.79667\)
1815.d5	1815a4	\([1, 1, 0, -1212, 7011]\)	\(111284641/50625\)	\(89685275625\)	\([2, 2]\)	\(1280\)	\(0.79667\)
1815.d6	1815a2	\([1, 1, 0, -607, -5936]\)	\(13997521/225\)	\(398601225\)	\([2, 2]\)	\(640\)	\(0.45010\)
1815.d7	1815a1	\([1, 1, 0, -2, -249]\)	\(-1/15\)	\(-26573415\)	\([2]\)	\(320\)	\(0.10352\)	\(\Gamma_0(N)\)-optimal
1815.d8	1815a6	\([1, 1, 0, 4233, 58194]\)	\(4733169839/3515625\)	\(-6228144140625\)	\([2]\)	\(2560\)	\(1.1432\)

Rank

The elliptic curves in class 1815.d have rank \(1\).

Complex multiplication

The elliptic curves in class 1815.d do not have complex multiplication.

Modular form 1815.2.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 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.