# Properties

 Label 34969.m Number of curves 3 Conductor 34969 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("34969.m1")

sage: E.isogeny_class()

## Elliptic curves in class 34969.m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
34969.m1 34969h3 [0, 1, 1, -273469236, 1740556342399] [] 3072000
34969.m2 34969h2 [0, 1, 1, -361346, 151310539] [] 614400
34969.m3 34969h1 [0, 1, 1, -11656, -1154301] [] 122880 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 34969.m have rank $$0$$.

## Modular form 34969.2.a.m

sage: E.q_eigenform(10)

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

## 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 LMFDB 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 LMFDB labels. 