# Properties

 Label 93600dp Number of curves $4$ Conductor $93600$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("dp1")

sage: E.isogeny_class()

## Elliptic curves in class 93600dp

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
93600.k3 93600dp1 $$[0, 0, 0, -3660825, 1525579000]$$ $$7442744143086784/2927948765625$$ $$2134474650140625000000$$ $$[2, 2]$$ $$4718592$$ $$2.7912$$ $$\Gamma_0(N)$$-optimal
93600.k4 93600dp2 $$[0, 0, 0, 11739300, 11012056000]$$ $$3834800837445824/3342041015625$$ $$-155926265625000000000000$$ $$[2]$$ $$9437184$$ $$3.1378$$
93600.k2 93600dp3 $$[0, 0, 0, -26442075, -51258577250]$$ $$350584567631475848/8259273550125$$ $$48168083344329000000000$$ $$[2]$$ $$9437184$$ $$3.1378$$
93600.k1 93600dp4 $$[0, 0, 0, -51192075, 140934735250]$$ $$2543984126301795848/909361981125$$ $$5303399073921000000000$$ $$[2]$$ $$9437184$$ $$3.1378$$

## Rank

sage: E.rank()

The elliptic curves in class 93600dp have rank $$1$$.

## Complex multiplication

The elliptic curves in class 93600dp do not have complex multiplication.

## Modular form 93600.2.a.dp

sage: E.q_eigenform(10)

$$q - 4q^{7} - q^{13} + 2q^{17} + 8q^{19} + O(q^{20})$$

## 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 Cremona numbering.

$$\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.