# Properties

 Label 92400.ik Number of curves $4$ Conductor $92400$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("ik1")

sage: E.isogeny_class()

## Elliptic curves in class 92400.ik

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
92400.ik1 92400cq4 $$[0, 1, 0, -176408, 28459188]$$ $$18972782339618/396165$$ $$12677280000000$$ $$$$ $$491520$$ $$1.6327$$
92400.ik2 92400cq3 $$[0, 1, 0, -46408, -3440812]$$ $$345431270018/41507235$$ $$1328231520000000$$ $$$$ $$491520$$ $$1.6327$$
92400.ik3 92400cq2 $$[0, 1, 0, -11408, 409188]$$ $$10262905636/1334025$$ $$21344400000000$$ $$[2, 2]$$ $$245760$$ $$1.2861$$
92400.ik4 92400cq1 $$[0, 1, 0, 1092, 34188]$$ $$35969456/144375$$ $$-577500000000$$ $$$$ $$122880$$ $$0.93951$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 92400.2.a.ik

sage: E.q_eigenform(10)

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