# Properties

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

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

sage: E.isogeny_class()

## Elliptic curves in class 100800.r

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
100800.r1 100800mi4 $$[0, 0, 0, -91854000300, -10715075262502000]$$ $$229625675762164624948320008/9568125$$ $$3571283520000000000$$ $$$$ $$165150720$$ $$4.4606$$
100800.r2 100800mi2 $$[0, 0, 0, -5740875300, -167423033752000]$$ $$448487713888272974160064/91549016015625$$ $$4271310891225000000000000$$ $$[2, 2]$$ $$82575360$$ $$4.1140$$
100800.r3 100800mi3 $$[0, 0, 0, -5721192300, -168628066378000]$$ $$-55486311952875723077768/801237030029296875$$ $$-299060118984375000000000000000$$ $$$$ $$165150720$$ $$4.4606$$
100800.r4 100800mi1 $$[0, 0, 0, -360035175, -2597139043000]$$ $$7079962908642659949376/100085966990454375$$ $$72962669936041239375000000$$ $$$$ $$41287680$$ $$3.7674$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

The elliptic curves in class 100800.r do not have complex multiplication.

## 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. 