# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("v1")

sage: E.isogeny_class()

## Elliptic curves in class 369600.v

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
369600.v1 369600v1 $$[0, -1, 0, -153281633, -293323828863]$$ $$388950302854250851396/188776686710390625$$ $$193307327191440000000000000$$ $$$$ $$113541120$$ $$3.7374$$ $$\Gamma_0(N)$$-optimal
369600.v2 369600v2 $$[0, -1, 0, 555306367, -2241232240863]$$ $$9246805402538461809742/6410550311279296875$$ $$-13128807037500000000000000000$$ $$$$ $$227082240$$ $$4.0839$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 369600.2.a.v

sage: E.q_eigenform(10)

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

## 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. 