# Properties

 Label 58800.jh Number of curves $4$ Conductor $58800$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("jh1")

sage: E.isogeny_class()

## Elliptic curves in class 58800.jh

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
58800.jh1 58800iu4 [0, 1, 0, -7321008, 7621931988]  1769472
58800.jh2 58800iu2 [0, 1, 0, -461008, 117091988] [2, 2] 884736
58800.jh3 58800iu1 [0, 1, 0, -69008, -4428012]  442368 $$\Gamma_0(N)$$-optimal
58800.jh4 58800iu3 [0, 1, 0, 126992, 395803988]  1769472

## Rank

sage: E.rank()

The elliptic curves in class 58800.jh have rank $$0$$.

## Complex multiplication

The elliptic curves in class 58800.jh do not have complex multiplication.

## Modular form 58800.2.a.jh

sage: E.q_eigenform(10)

$$q + q^{3} + q^{9} + 4q^{11} - 2q^{13} - 6q^{17} + O(q^{20})$$

## 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. 