# Properties

 Label 45968.t Number of curves 4 Conductor 45968 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("45968.t1")

sage: E.isogeny_class()

## Elliptic curves in class 45968.t

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
45968.t1 45968k4 [0, -1, 0, -305608, 45037680]  663552
45968.t2 45968k3 [0, -1, 0, -278568, 56675696]  331776
45968.t3 45968k2 [0, -1, 0, -116328, -15229072]  221184
45968.t4 45968k1 [0, -1, 0, -8168, -173200]  110592 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 45968.t have rank $$0$$.

## Modular form 45968.2.a.t

sage: E.q_eigenform(10)

$$q + 2q^{3} - 4q^{7} + q^{9} + 6q^{11} - q^{17} - 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 