# Properties

 Label 1936g Number of curves 3 Conductor 1936 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("1936.i1")

sage: E.isogeny_class()

## Elliptic curves in class 1936g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1936.i3 1936g1 [0, 1, 0, -645, 14771] [] 960 $$\Gamma_0(N)$$-optimal
1936.i2 1936g2 [0, 1, 0, -20005, -1979309] [] 4800
1936.i1 1936g3 [0, 1, 0, -15140165, -22679876749] [] 24000

## Rank

sage: E.rank()

The elliptic curves in class 1936g have rank $$1$$.

## Modular form1936.2.a.i

sage: E.q_eigenform(10)

$$q + q^{3} + q^{5} - 2q^{7} - 2q^{9} - 4q^{13} + q^{15} + 2q^{17} + O(q^{20})$$

## 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 Cremona numbering.

$$\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 