# Properties

 Label 142296h Number of curves 4 Conductor 142296 CM no Rank 1 Graph

# Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("142296.cs1")

sage: E.isogeny_class()

## Elliptic curves in class 142296h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
142296.cs3 142296h1 [0, 1, 0, -73124, -7362720] [2] 737280 $$\Gamma_0(N)$$-optimal
142296.cs2 142296h2 [0, 1, 0, -191704, 22424576] [2, 2] 1474560
142296.cs1 142296h3 [0, 1, 0, -2800464, 1802642400] [2] 2949120
142296.cs4 142296h4 [0, 1, 0, 519776, 150490976] [2] 2949120

## Rank

sage: E.rank()

The elliptic curves in class 142296h have rank $$1$$.

## Modular form 142296.2.a.cs

sage: E.q_eigenform(10)

$$q + q^{3} - 2q^{5} + q^{9} + 2q^{13} - 2q^{15} + 6q^{17} + O(q^{20})$$

## 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 Cremona 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 Cremona labels.