# Properties

 Label 10830.h Number of curves $4$ Conductor $10830$ CM no Rank $1$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 10830.h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10830.h1 10830h3 $$[1, 1, 0, -1097447, -442967949]$$ $$3107086841064961/570$$ $$26816152170$$ $$$$ $$138240$$ $$1.8367$$
10830.h2 10830h4 $$[1, 1, 0, -79427, -4617201]$$ $$1177918188481/488703750$$ $$22991498466753750$$ $$$$ $$138240$$ $$1.8367$$
10830.h3 10830h2 $$[1, 1, 0, -68597, -6941319]$$ $$758800078561/324900$$ $$15285206736900$$ $$[2, 2]$$ $$69120$$ $$1.4902$$
10830.h4 10830h1 $$[1, 1, 0, -3617, -144411]$$ $$-111284641/123120$$ $$-5792288868720$$ $$$$ $$34560$$ $$1.1436$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 10830.h have rank $$1$$.

## Complex multiplication

The elliptic curves in class 10830.h do not have complex multiplication.

## Modular form 10830.2.a.h

sage: E.q_eigenform(10)

$$q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} + 4q^{7} - q^{8} + q^{9} - q^{10} - 4q^{11} - q^{12} + 2q^{13} - 4q^{14} - q^{15} + q^{16} - 2q^{17} - q^{18} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 