# Properties

 Label 11830l Number of curves $4$ Conductor $11830$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("11830.h1")

sage: E.isogeny_class()

## Elliptic curves in class 11830l

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
11830.h4 11830l1 [1, -1, 0, 391, -4835]  7680 $$\Gamma_0(N)$$-optimal
11830.h3 11830l2 [1, -1, 0, -2989, -50127] [2, 2] 15360
11830.h1 11830l3 [1, -1, 0, -45239, -3692077]  30720
11830.h2 11830l4 [1, -1, 0, -14819, 652575]  30720

## Rank

sage: E.rank()

The elliptic curves in class 11830l have rank $$1$$.

## Modular form 11830.2.a.h

sage: E.q_eigenform(10)

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

## 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 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. 