# Properties

 Label 369600.ta Number of curves $4$ Conductor $369600$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("ta1")

sage: E.isogeny_class()

## Elliptic curves in class 369600.ta

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
369600.ta1 369600ta4 $$[0, 1, 0, -439605633, -3547797883137]$$ $$9175156963749600923236/50249267578125$$ $$51455250000000000000000$$ $$[2]$$ $$70778880$$ $$3.5514$$
369600.ta2 369600ta3 $$[0, 1, 0, -88713633, 257610304863]$$ $$75404081626158563716/15633273575910375$$ $$16008472141732224000000000$$ $$[2]$$ $$70778880$$ $$3.5514$$
369600.ta3 369600ta2 $$[0, 1, 0, -27963633, -53368945137]$$ $$9446361110552374864/661910688140625$$ $$169449136164000000000000$$ $$[2, 2]$$ $$35389440$$ $$3.2048$$
369600.ta4 369600ta1 $$[0, 1, 0, 1560867, -3620162637]$$ $$26284586405881856/369163298455875$$ $$-5906612775294000000000$$ $$[2]$$ $$17694720$$ $$2.8582$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 369600.ta have rank $$0$$.

## Complex multiplication

The elliptic curves in class 369600.ta do not have complex multiplication.

## Modular form 369600.2.a.ta

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.