# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("t1")

sage: E.isogeny_class()

## Elliptic curves in class 92400t

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
92400.ct3 92400t1 $$[0, -1, 0, -14674308, 21641270112]$$ $$87364831012240243408/1760913$$ $$7043652000000$$ $$$$ $$2949120$$ $$2.4487$$ $$\Gamma_0(N)$$-optimal
92400.ct2 92400t2 $$[0, -1, 0, -14674808, 21639722112]$$ $$21843440425782779332/3100814593569$$ $$49613033497104000000$$ $$[2, 2]$$ $$5898240$$ $$2.7953$$
92400.ct4 92400t3 $$[0, -1, 0, -13351808, 25698686112]$$ $$-8226100326647904626/4152140742401883$$ $$-132868503756860256000000$$ $$$$ $$11796480$$ $$3.1419$$
92400.ct1 92400t4 $$[0, -1, 0, -16005808, 17481678112]$$ $$14171198121996897746/4077720290568771$$ $$130487049298200672000000$$ $$$$ $$11796480$$ $$3.1419$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 92400.2.a.t

sage: E.q_eigenform(10)

$$q - q^{3} + q^{7} + q^{9} - q^{11} + 6q^{13} + 2q^{17} + 8q^{19} + O(q^{20})$$ ## 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. 