# Properties

 Label 92400.t Number of curves $4$ Conductor $92400$ CM no Rank $1$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 92400.t

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
92400.t1 92400ez4 $$[0, -1, 0, -106476448, -422843595008]$$ $$260744057755293612689909/8504954620259328$$ $$4354536765572775936000$$ $$$$ $$9216000$$ $$3.2462$$
92400.t2 92400ez3 $$[0, -1, 0, -6943648, -6000228608]$$ $$72313087342699809269/11447096545640448$$ $$5860913431367909376000$$ $$$$ $$4608000$$ $$2.8996$$
92400.t3 92400ez2 $$[0, -1, 0, -1884048, 986880192]$$ $$1444540994277943589/15251205665388$$ $$7808617300678656000$$ $$$$ $$1843200$$ $$2.4414$$
92400.t4 92400ez1 $$[0, -1, 0, -1879248, 992198592]$$ $$1433528304665250149/162339408$$ $$83117776896000$$ $$$$ $$921600$$ $$2.0949$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 92400.2.a.t

sage: E.q_eigenform(10)

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

$$\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 