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

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

Elliptic curves in class 1815a

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

Rank

The elliptic curves in class 1815a have rank $1$.

Complex multiplication

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

Modular form 1815.2.a.a

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.