# Properties

 Label 30899c Number of curves 3 Conductor 30899 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("30899.f1")

sage: E.isogeny_class()

## Elliptic curves in class 30899c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
30899.f3 30899c1 [0, 1, 1, -936, 25879] [] 29952 $$\Gamma_0(N)$$-optimal
30899.f2 30899c2 [0, 1, 1, -29026, -3457281] [] 149760
30899.f1 30899c3 [0, 1, 1, -21967316, -39636368621] [] 748800

## Rank

sage: E.rank()

The elliptic curves in class 30899c have rank $$0$$.

## Modular form 30899.2.a.f

sage: E.q_eigenform(10)

$$q + 2q^{2} + q^{3} + 2q^{4} - q^{5} + 2q^{6} - 2q^{7} - 2q^{9} - 2q^{10} + q^{11} + 2q^{12} + 4q^{13} - 4q^{14} - q^{15} - 4q^{16} - 2q^{17} - 4q^{18} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 