# Properties

 Label 37030t Number of curves $4$ Conductor $37030$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("37030.s1")

sage: E.isogeny_class()

## Elliptic curves in class 37030t

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
37030.s4 37030t1 [1, -1, 1, 1223, 25929]  50688 $$\Gamma_0(N)$$-optimal
37030.s3 37030t2 [1, -1, 1, -9357, 284081] [2, 2] 101376
37030.s2 37030t3 [1, -1, 1, -46387, -3581851]  202752
37030.s1 37030t4 [1, -1, 1, -141607, 20544781]  202752

## Rank

sage: E.rank()

The elliptic curves in class 37030t have rank $$1$$.

## Modular form 37030.2.a.s

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + q^{5} + q^{7} + q^{8} - 3q^{9} + q^{10} - 4q^{11} - 6q^{13} + q^{14} + q^{16} - 2q^{17} - 3q^{18} + O(q^{20})$$

## 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. 