# Properties

 Label 369600.ws Number of curves $4$ Conductor $369600$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("ws1")

sage: E.isogeny_class()

## Elliptic curves in class 369600.ws

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
369600.ws1 369600ws4 $$[0, 1, 0, -78848033, -269511167937]$$ $$13235378341603461121/9240$$ $$37847040000000$$ $$$$ $$14155776$$ $$2.8184$$
369600.ws2 369600ws2 $$[0, 1, 0, -4928033, -4212287937]$$ $$3231355012744321/85377600$$ $$349706649600000000$$ $$[2, 2]$$ $$7077888$$ $$2.4718$$
369600.ws3 369600ws3 $$[0, 1, 0, -4736033, -4555391937]$$ $$-2868190647517441/527295615000$$ $$-2159802839040000000000$$ $$$$ $$14155776$$ $$2.8184$$
369600.ws4 369600ws1 $$[0, 1, 0, -320033, -60479937]$$ $$885012508801/127733760$$ $$523197480960000000$$ $$$$ $$3538944$$ $$2.1253$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 369600.2.a.ws

sage: E.q_eigenform(10)

$$q + q^{3} + q^{7} + q^{9} + q^{11} + 2 q^{13} + 2 q^{17} - 4 q^{19} + O(q^{20})$$

## 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. 