# Properties

 Label 100800.r Number of curves 4 Conductor 100800 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("100800.r1")

sage: E.isogeny_class()

## Elliptic curves in class 100800.r

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
100800.r1 100800mi4 [0, 0, 0, -91854000300, -10715075262502000]  165150720
100800.r2 100800mi2 [0, 0, 0, -5740875300, -167423033752000] [2, 2] 82575360
100800.r3 100800mi3 [0, 0, 0, -5721192300, -168628066378000]  165150720
100800.r4 100800mi1 [0, 0, 0, -360035175, -2597139043000]  41287680 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 100800.r have rank $$1$$.

## Modular form 100800.2.a.r

sage: E.q_eigenform(10)

$$q - q^{7} - 4q^{11} - 6q^{13} + 6q^{17} + 4q^{19} + O(q^{20})$$

## 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. 