# Properties

 Label 4356.d Number of curves 2 Conductor 4356 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("4356.d1")

sage: E.isogeny_class()

## Elliptic curves in class 4356.d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
4356.d1 4356f2 [0, 0, 0, -13431, -284834]  11520
4356.d2 4356f1 [0, 0, 0, 2904, -33275]  5760 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 4356.d have rank $$0$$.

## Modular form4356.2.a.d

sage: E.q_eigenform(10)

$$q - 2q^{5} + 2q^{7} + 2q^{13} + 4q^{17} + 6q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 