# Properties

 Label 17457a Number of curves 4 Conductor 17457 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("17457.c1")

sage: E.isogeny_class()

## Elliptic curves in class 17457a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
17457.c3 17457a1 [1, 1, 0, -3449, 75888]  16896 $$\Gamma_0(N)$$-optimal
17457.c2 17457a2 [1, 1, 0, -6094, -60065] [2, 2] 33792
17457.c1 17457a3 [1, 1, 0, -77509, -8329922]  67584
17457.c4 17457a4 [1, 1, 0, 23001, -438300]  67584

## Rank

sage: E.rank()

The elliptic curves in class 17457a have rank $$0$$.

## Modular form 17457.2.a.c

sage: E.q_eigenform(10)

$$q + q^{2} - q^{3} - q^{4} + 2q^{5} - q^{6} - 4q^{7} - 3q^{8} + q^{9} + 2q^{10} - q^{11} + q^{12} - 2q^{13} - 4q^{14} - 2q^{15} - q^{16} + 2q^{17} + q^{18} + O(q^{20})$$

## 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. 