Properties

 Label 28224fv Number of curves $6$ Conductor $28224$ CM no Rank $0$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("fv1")

sage: E.isogeny_class()

Elliptic curves in class 28224fv

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
28224.et5 28224fv1 $$[0, 0, 0, 1176, -19208]$$ $$2048/3$$ $$-263473523712$$ $$[2]$$ $$24576$$ $$0.87691$$ $$\Gamma_0(N)$$-optimal
28224.et4 28224fv2 $$[0, 0, 0, -7644, -192080]$$ $$35152/9$$ $$12646729138176$$ $$[2, 2]$$ $$49152$$ $$1.2235$$
28224.et3 28224fv3 $$[0, 0, 0, -42924, 3265360]$$ $$1556068/81$$ $$455282248974336$$ $$[2, 2]$$ $$98304$$ $$1.5701$$
28224.et2 28224fv4 $$[0, 0, 0, -113484, -14713328]$$ $$28756228/3$$ $$16862305517568$$ $$[2]$$ $$98304$$ $$1.5701$$
28224.et6 28224fv5 $$[0, 0, 0, 27636, 12946192]$$ $$207646/6561$$ $$-73755724333842432$$ $$[2]$$ $$196608$$ $$1.9166$$
28224.et1 28224fv6 $$[0, 0, 0, -677964, 214860688]$$ $$3065617154/9$$ $$101173833105408$$ $$[2]$$ $$196608$$ $$1.9166$$

Rank

sage: E.rank()

The elliptic curves in class 28224fv have rank $$0$$.

Complex multiplication

The elliptic curves in class 28224fv do not have complex multiplication.

Modular form 28224.2.a.fv

sage: E.q_eigenform(10)

$$q + 2q^{5} - 4q^{11} - 2q^{13} + 2q^{17} + 4q^{19} + O(q^{20})$$

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.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)$$

Isogeny graph

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

The vertices are labelled with Cremona labels.