# Properties

 Label 2925.d Number of curves $8$ Conductor $2925$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("d1")

sage: E.isogeny_class()

## Elliptic curves in class 2925.d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2925.d1 2925g7 $$[1, -1, 1, -29250005, 60896057622]$$ $$242970740812818720001/24375$$ $$277646484375$$ $$[2]$$ $$73728$$ $$2.5434$$
2925.d2 2925g5 $$[1, -1, 1, -1828130, 951838872]$$ $$59319456301170001/594140625$$ $$6767633056640625$$ $$[2, 2]$$ $$36864$$ $$2.1969$$
2925.d3 2925g8 $$[1, -1, 1, -1784255, 999662622]$$ $$-55150149867714721/5950927734375$$ $$-67784786224365234375$$ $$[2]$$ $$73728$$ $$2.5434$$
2925.d4 2925g3 $$[1, -1, 1, -117005, 14142372]$$ $$15551989015681/1445900625$$ $$16469711806640625$$ $$[2, 2]$$ $$18432$$ $$1.8503$$
2925.d5 2925g2 $$[1, -1, 1, -25880, -1348878]$$ $$168288035761/27720225$$ $$315750687890625$$ $$[2, 2]$$ $$9216$$ $$1.5037$$
2925.d6 2925g1 $$[1, -1, 1, -24755, -1492878]$$ $$147281603041/5265$$ $$59971640625$$ $$[2]$$ $$4608$$ $$1.1571$$ $$\Gamma_0(N)$$-optimal
2925.d7 2925g4 $$[1, -1, 1, 47245, -7637628]$$ $$1023887723039/2798036865$$ $$-31871388665390625$$ $$[2]$$ $$18432$$ $$1.8503$$
2925.d8 2925g6 $$[1, -1, 1, 136120, 66792372]$$ $$24487529386319/183539412225$$ $$-2090628617375390625$$ $$[2]$$ $$36864$$ $$2.1969$$

## Rank

sage: E.rank()

The elliptic curves in class 2925.d have rank $$0$$.

## Complex multiplication

The elliptic curves in class 2925.d do not have complex multiplication.

## Modular form2925.2.a.d

sage: E.q_eigenform(10)

$$q - q^{2} - q^{4} + 3 q^{8} - 4 q^{11} - q^{13} - q^{16} + 2 q^{17} - 4 q^{19} + O(q^{20})$$

## Isogeny matrix

sage: E.isogeny_class().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.

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

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with LMFDB labels.