# Properties

 Label 130130.h Number of curves 4 Conductor 130130 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("130130.h1")

sage: E.isogeny_class()

## Elliptic curves in class 130130.h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
130130.h1 130130h4 [1, 0, 1, -4413608, -3468173382]  7464960
130130.h2 130130h2 [1, 0, 1, -604348, 179176506]  2488320
130130.h3 130130h1 [1, 0, 1, -9468, 6899258]  1244160 $$\Gamma_0(N)$$-optimal
130130.h4 130130h3 [1, 0, 1, 85172, -185863494]  3732480

## Rank

sage: E.rank()

The elliptic curves in class 130130.h have rank $$1$$.

## Modular form 130130.2.a.h

sage: E.q_eigenform(10)

$$q - q^{2} - 2q^{3} + q^{4} + q^{5} + 2q^{6} - q^{7} - q^{8} + q^{9} - q^{10} + q^{11} - 2q^{12} + q^{14} - 2q^{15} + q^{16} - q^{18} + 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 