# Properties

 Label 92400hd Number of curves $6$ Conductor $92400$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("hd1")

sage: E.isogeny_class()

## Elliptic curves in class 92400hd

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
92400.ia6 92400hd1 [0, 1, 0, 13992, 185051988] [2] 1474560 $$\Gamma_0(N)$$-optimal
92400.ia5 92400hd2 [0, 1, 0, -4788008, 3959423988] [2, 2] 2949120
92400.ia4 92400hd3 [0, 1, 0, -10178008, -6594196012] [2] 5898240
92400.ia2 92400hd4 [0, 1, 0, -76230008, 256149683988] [2, 2] 5898240
92400.ia3 92400hd5 [0, 1, 0, -75852008, 258816095988] [2] 11796480
92400.ia1 92400hd6 [0, 1, 0, -1219680008, 16394802983988] [2] 11796480

## Rank

sage: E.rank()

The elliptic curves in class 92400hd have rank $$1$$.

## Complex multiplication

The elliptic curves in class 92400hd do not have complex multiplication.

## Modular form 92400.2.a.hd

sage: E.q_eigenform(10)

$$q + q^{3} + q^{7} + q^{9} + q^{11} + 2q^{13} - 2q^{17} - 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.