# Properties

 Label 36100.a Number of curves 4 Conductor 36100 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("36100.a1")

sage: E.isogeny_class()

## Elliptic curves in class 36100.a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
36100.a1 36100j3 [0, 1, 0, -373033, 87550188]  248832
36100.a2 36100j4 [0, 1, 0, -327908, 109571188]  497664
36100.a3 36100j1 [0, 1, 0, -12033, -353312]  82944 $$\Gamma_0(N)$$-optimal
36100.a4 36100j2 [0, 1, 0, 33092, -2338812]  165888

## Rank

sage: E.rank()

The elliptic curves in class 36100.a have rank $$1$$.

## Modular form 36100.2.a.a

sage: E.q_eigenform(10)

$$q - 2q^{3} - 2q^{7} + q^{9} + 2q^{13} + 6q^{17} + O(q^{20})$$

## 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 LMFDB numbering.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with LMFDB labels. 