# Properties

 Label 3600.h Number of curves 4 Conductor 3600 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("3600.h1")

sage: E.isogeny_class()

## Elliptic curves in class 3600.h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
3600.h1 3600p3 [0, 0, 0, -24075, -1437750]  6144
3600.h2 3600p2 [0, 0, 0, -1575, -20250] [2, 2] 3072
3600.h3 3600p1 [0, 0, 0, -450, 3375]  1536 $$\Gamma_0(N)$$-optimal
3600.h4 3600p4 [0, 0, 0, 2925, -114750]  6144

## Rank

sage: E.rank()

The elliptic curves in class 3600.h have rank $$0$$.

## Modular form3600.2.a.h

sage: E.q_eigenform(10)

$$q - 4q^{7} + 4q^{11} + 2q^{13} + 2q^{17} - 4q^{19} + O(q^{20})$$

## 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 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. 