# Properties

 Label 92400dk Number of curves $6$ Conductor $92400$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("92400.q1")

sage: E.isogeny_class()

## Elliptic curves in class 92400dk

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
92400.q4 92400dk1 [0, -1, 0, -106008, -13249488] [2] 393216 $$\Gamma_0(N)$$-optimal
92400.q3 92400dk2 [0, -1, 0, -108008, -12721488] [2, 2] 786432
92400.q5 92400dk3 [0, -1, 0, 101992, -56401488] [2] 1572864
92400.q2 92400dk4 [0, -1, 0, -350008, 64718512] [2, 2] 1572864
92400.q6 92400dk5 [0, -1, 0, 727992, 383806512] [2] 3145728
92400.q1 92400dk6 [0, -1, 0, -5300008, 4697918512] [2] 3145728

## Rank

sage: E.rank()

The elliptic curves in class 92400dk have rank $$0$$.

## Modular form 92400.2.a.q

sage: E.q_eigenform(10)

$$q - q^{3} - q^{7} + q^{9} - q^{11} + 2q^{13} + 6q^{17} + 4q^{19} + O(q^{20})$$

## 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.