# Properties

 Label 132600.r Number of curves $4$ Conductor $132600$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("r1")

sage: E.isogeny_class()

## Elliptic curves in class 132600.r

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
132600.r1 132600t4 $$[0, -1, 0, -817408, -284175188]$$ $$1887517194957938/21849165$$ $$699173280000000$$ $$$$ $$1179648$$ $$1.9996$$
132600.r2 132600t2 $$[0, -1, 0, -52408, -4185188]$$ $$994958062276/98903025$$ $$1582448400000000$$ $$[2, 2]$$ $$589824$$ $$1.6530$$
132600.r3 132600t1 $$[0, -1, 0, -11908, 431812]$$ $$46689225424/7249905$$ $$28999620000000$$ $$$$ $$294912$$ $$1.3064$$ $$\Gamma_0(N)$$-optimal
132600.r4 132600t3 $$[0, -1, 0, 64592, -20331188]$$ $$931329171502/6107473125$$ $$-195439140000000000$$ $$$$ $$1179648$$ $$1.9996$$

## Rank

sage: E.rank()

The elliptic curves in class 132600.r have rank $$1$$.

## Complex multiplication

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

## Modular form 132600.2.a.r

sage: E.q_eigenform(10)

$$q - q^{3} + q^{9} + 4q^{11} + q^{13} - q^{17} + 8q^{19} + O(q^{20})$$ ## 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. 