# Properties

 Label 4368.c Number of curves $2$ Conductor $4368$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
E = EllipticCurve("c1")

E.isogeny_class()

## Elliptic curves in class 4368.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4368.c1 4368s2 $$[0, -1, 0, -404, -2436]$$ $$28556329552/5373459$$ $$1375605504$$ $$$$ $$1920$$ $$0.47132$$
4368.c2 4368s1 $$[0, -1, 0, 51, -252]$$ $$899022848/2012283$$ $$-32196528$$ $$$$ $$960$$ $$0.12475$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 4368.c have rank $$1$$.

## Complex multiplication

The elliptic curves in class 4368.c do not have complex multiplication.

## Modular form4368.2.a.c

sage: E.q_eigenform(10)

$$q - q^{3} - 2 q^{5} + q^{7} + q^{9} - q^{13} + 2 q^{15} - 4 q^{17} + 8 q^{19} + O(q^{20})$$

## 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. 