# Properties

 Label 53816.d Number of curves $4$ Conductor $53816$ CM no Rank $1$ Graph # Learn more

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

sage: E.isogeny_class()

## Elliptic curves in class 53816.d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
53816.d1 53816c4 $$[0, 0, 0, -287339, -59284090]$$ $$1443468546/7$$ $$12723252770816$$ $$$$ $$230400$$ $$1.7150$$
53816.d2 53816c3 $$[0, 0, 0, -56699, 4111158]$$ $$11090466/2401$$ $$4364075700389888$$ $$$$ $$230400$$ $$1.7150$$
53816.d3 53816c2 $$[0, 0, 0, -18259, -893730]$$ $$740772/49$$ $$44531384697856$$ $$[2, 2]$$ $$115200$$ $$1.3684$$
53816.d4 53816c1 $$[0, 0, 0, 961, -59582]$$ $$432/7$$ $$-1590406596352$$ $$$$ $$57600$$ $$1.0218$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 53816.d have rank $$1$$.

## Complex multiplication

The elliptic curves in class 53816.d do not have complex multiplication.

## Modular form 53816.2.a.d

sage: E.q_eigenform(10)

$$q + 2q^{5} - q^{7} - 3q^{9} + 4q^{11} - 2q^{13} + 6q^{17} + 8q^{19} + O(q^{20})$$ ## 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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 