# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("4356.c1")

sage: E.isogeny_class()

## Elliptic curves in class 4356.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
4356.c1 4356g2 [0, 0, 0, -1407351, 642598814]  57600
4356.c2 4356g1 [0, 0, 0, -84216, 10934165]  28800 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form4356.2.a.c

sage: E.q_eigenform(10)

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

## 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. 