# Properties

 Label 327990.d Number of curves $4$ Conductor $327990$ CM no Rank $0$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 327990.d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
327990.d1 327990d4 $$[1, 1, 0, -1005853, -368944997]$$ $$189208196468929/10860320250$$ $$6459971758228550250$$ $$[2]$$ $$7257600$$ $$2.3635$$
327990.d2 327990d2 $$[1, 1, 0, -173263, 27564637]$$ $$967068262369/4928040$$ $$2931313118820840$$ $$[2]$$ $$2419200$$ $$1.8142$$
327990.d3 327990d1 $$[1, 1, 0, -5063, 888117]$$ $$-24137569/561600$$ $$-334052777073600$$ $$[2]$$ $$1209600$$ $$1.4676$$ $$\Gamma_0(N)$$-optimal
327990.d4 327990d3 $$[1, 1, 0, 45397, -23504247]$$ $$17394111071/411937500$$ $$-245030031794437500$$ $$[2]$$ $$3628800$$ $$2.0169$$

## Rank

sage: E.rank()

The elliptic curves in class 327990.d have rank $$0$$.

## Complex multiplication

The elliptic curves in class 327990.d do not have complex multiplication.

## Modular form 327990.2.a.d

sage: E.q_eigenform(10)

$$q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} + 2 q^{7} - q^{8} + q^{9} + q^{10} - q^{12} + q^{13} - 2 q^{14} + q^{15} + q^{16} - q^{18} - 2 q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.