# Properties

 Label 51600.dq Number of curves $4$ Conductor $51600$ CM no Rank $0$ Graph # Learn more

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

sage: E.isogeny_class()

## Elliptic curves in class 51600.dq

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
51600.dq1 51600di4 $$[0, 1, 0, -2073008, 990587988]$$ $$15393836938735081/2275690697640$$ $$145644204648960000000$$ $$$$ $$1658880$$ $$2.5936$$
51600.dq2 51600di3 $$[0, 1, 0, -1993008, 1082267988]$$ $$13679527032530281/381633600$$ $$24424550400000000$$ $$$$ $$829440$$ $$2.2471$$
51600.dq3 51600di2 $$[0, 1, 0, -543008, -154032012]$$ $$276670733768281/336980250$$ $$21566736000000000$$ $$$$ $$552960$$ $$2.0443$$
51600.dq4 51600di1 $$[0, 1, 0, -43008, -1032012]$$ $$137467988281/72562500$$ $$4644000000000000$$ $$$$ $$276480$$ $$1.6978$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 51600.dq have rank $$0$$.

## Complex multiplication

The elliptic curves in class 51600.dq do not have complex multiplication.

## Modular form 51600.2.a.dq

sage: E.q_eigenform(10)

$$q + q^{3} + 2q^{7} + q^{9} + 6q^{11} - 2q^{13} - 2q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 