# Properties

 Label 5808.t Number of curves 4 Conductor 5808 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("5808.t1")

sage: E.isogeny_class()

## Elliptic curves in class 5808.t

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
5808.t1 5808bg3 [0, 1, 0, -283664, 57999060]  46080
5808.t2 5808bg2 [0, 1, 0, -22304, 395316] [2, 2] 23040
5808.t3 5808bg1 [0, 1, 0, -12624, -545580]  11520 $$\Gamma_0(N)$$-optimal
5808.t4 5808bg4 [0, 1, 0, 84176, 3163796]  46080

## Rank

sage: E.rank()

The elliptic curves in class 5808.t have rank $$0$$.

## Modular form5808.2.a.t

sage: E.q_eigenform(10)

$$q + q^{3} - 2q^{5} + 4q^{7} + q^{9} + 2q^{13} - 2q^{15} + 2q^{17} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 