# Properties

 Label 24200h Number of curves 4 Conductor 24200 CM no Rank 2 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("24200.n1")

sage: E.isogeny_class()

## Elliptic curves in class 24200h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
24200.n3 24200h1 [0, 0, 0, -6050, -166375]  30720 $$\Gamma_0(N)$$-optimal
24200.n2 24200h2 [0, 0, 0, -21175, 998250] [2, 2] 61440
24200.n4 24200h3 [0, 0, 0, 39325, 5656750]  122880
24200.n1 24200h4 [0, 0, 0, -323675, 70875750]  122880

## Rank

sage: E.rank()

The elliptic curves in class 24200h have rank $$2$$.

## Modular form 24200.2.a.n

sage: E.q_eigenform(10)

$$q - 4q^{7} - 3q^{9} - 2q^{13} + 2q^{17} - 4q^{19} + O(q^{20})$$

## 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 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. 