# Properties

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

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("dq1")

sage: E.isogeny_class()

## Elliptic curves in class 93600dq

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
93600.f3 93600dq1 $$[0, 0, 0, -48825, -4131000]$$ $$17657244864/105625$$ $$77000625000000$$ $$[2, 2]$$ $$393216$$ $$1.5041$$ $$\Gamma_0(N)$$-optimal
93600.f4 93600dq2 $$[0, 0, 0, -20700, -8856000]$$ $$-21024576/714025$$ $$-33313550400000000$$ $$[2]$$ $$786432$$ $$1.8507$$
93600.f2 93600dq3 $$[0, 0, 0, -78075, 1397250]$$ $$9024895368/5078125$$ $$29615625000000000$$ $$[2]$$ $$786432$$ $$1.8507$$
93600.f1 93600dq4 $$[0, 0, 0, -780075, -265187250]$$ $$9001508089608/325$$ $$1895400000000$$ $$[2]$$ $$786432$$ $$1.8507$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 93600.2.a.dq

sage: E.q_eigenform(10)

$$q - 4q^{7} - 4q^{11} - q^{13} + 2q^{17} - 4q^{19} + O(q^{20})$$

## 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.