# Properties

 Label 369600gr Number of curves $2$ Conductor $369600$ CM no Rank $2$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("gr1")

sage: E.isogeny_class()

## Elliptic curves in class 369600gr

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
369600.gr2 369600gr1 $$[0, -1, 0, -2133, 119637]$$ $$-67108864/343035$$ $$-5488560000000$$ $$$$ $$737280$$ $$1.1288$$ $$\Gamma_0(N)$$-optimal
369600.gr1 369600gr2 $$[0, -1, 0, -51633, 4525137]$$ $$59466754384/121275$$ $$31046400000000$$ $$$$ $$1474560$$ $$1.4754$$

## Rank

sage: E.rank()

The elliptic curves in class 369600gr have rank $$2$$.

## Complex multiplication

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

## Modular form 369600.2.a.gr

sage: E.q_eigenform(10)

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

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 