Properties

 Label 132600y Number of curves $4$ Conductor $132600$ CM no Rank $0$ Graph Related objects

Show commands: SageMath
sage: E = EllipticCurve("y1")

sage: E.isogeny_class()

Elliptic curves in class 132600y

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
132600.bb3 132600y1 $$[0, -1, 0, -783383, 267136512]$$ $$212670222886967296/616241925$$ $$154060481250000$$ $$$$ $$1179648$$ $$1.9524$$ $$\Gamma_0(N)$$-optimal
132600.bb2 132600y2 $$[0, -1, 0, -793508, 259887012]$$ $$13813960087661776/714574355625$$ $$2858297422500000000$$ $$[2, 2]$$ $$2359296$$ $$2.2990$$
132600.bb4 132600y3 $$[0, -1, 0, 506992, 1027182012]$$ $$900753985478876/29018422265625$$ $$-464294756250000000000$$ $$$$ $$4718592$$ $$2.6456$$
132600.bb1 132600y4 $$[0, -1, 0, -2256008, -971537988]$$ $$79364416584061444/20404090514925$$ $$326465448238800000000$$ $$$$ $$4718592$$ $$2.6456$$

Rank

sage: E.rank()

The elliptic curves in class 132600y have rank $$0$$.

Complex multiplication

The elliptic curves in class 132600y do not have complex multiplication.

Modular form 132600.2.a.y

sage: E.q_eigenform(10)

$$q - q^{3} + 4 q^{7} + q^{9} - q^{13} - q^{17} + O(q^{20})$$ 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 Cremona 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 Cremona labels. 