# Properties

 Label 72897.a Number of curves 4 Conductor 72897 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("72897.a1")

sage: E.isogeny_class()

## Elliptic curves in class 72897.a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
72897.a1 72897a4 [1, 1, 0, -323664, -70939863]  618240
72897.a2 72897a2 [1, 1, 0, -25449, -501480] [2, 2] 309120
72897.a3 72897a1 [1, 1, 0, -14404, 653827]  154560 $$\Gamma_0(N)$$-optimal
72897.a4 72897a3 [1, 1, 0, 96046, -3781845]  618240

## Rank

sage: E.rank()

The elliptic curves in class 72897.a have rank $$0$$.

## Modular form 72897.2.a.a

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 LMFDB 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 LMFDB labels. 