# Properties

 Label 22800.t Number of curves $4$ Conductor $22800$ CM no Rank $1$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 22800.t

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
22800.t1 22800ca4 $$[0, -1, 0, -248408, 47667312]$$ $$26487576322129/44531250$$ $$2850000000000000$$ $$[2]$$ $$147456$$ $$1.8608$$
22800.t2 22800ca2 $$[0, -1, 0, -20408, 243312]$$ $$14688124849/8122500$$ $$519840000000000$$ $$[2, 2]$$ $$73728$$ $$1.5142$$
22800.t3 22800ca1 $$[0, -1, 0, -12408, -524688]$$ $$3301293169/22800$$ $$1459200000000$$ $$[2]$$ $$36864$$ $$1.1676$$ $$\Gamma_0(N)$$-optimal
22800.t4 22800ca3 $$[0, -1, 0, 79592, 1843312]$$ $$871257511151/527800050$$ $$-33779203200000000$$ $$[2]$$ $$147456$$ $$1.8608$$

## Rank

sage: E.rank()

The elliptic curves in class 22800.t have rank $$1$$.

## Complex multiplication

The elliptic curves in class 22800.t do not have complex multiplication.

## Modular form 22800.2.a.t

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.