# Properties

 Label 369600.c Number of curves $2$ Conductor $369600$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("c1")

sage: E.isogeny_class()

## Elliptic curves in class 369600.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
369600.c1 369600c2 $$[0, -1, 0, -20273, -631983]$$ $$449955166736/174330387$$ $$357028632576000$$ $$$$ $$1720320$$ $$1.4913$$
369600.c2 369600c1 $$[0, -1, 0, 4027, -73083]$$ $$56409309184/50014503$$ $$-6401856384000$$ $$$$ $$860160$$ $$1.1447$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 369600.2.a.c

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 