# Properties

 Label 5600.c Number of curves $2$ Conductor $5600$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 5600.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5600.c1 5600p2 $$[0, 1, 0, -208, 588]$$ $$125000/49$$ $$392000000$$ $$$$ $$2304$$ $$0.34752$$
5600.c2 5600p1 $$[0, 1, 0, 42, 88]$$ $$8000/7$$ $$-7000000$$ $$$$ $$1152$$ $$0.00094497$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 5600.c have rank $$0$$.

## Complex multiplication

The elliptic curves in class 5600.c do not have complex multiplication.

## Modular form5600.2.a.c

sage: E.q_eigenform(10)

$$q - 2q^{3} - q^{7} + q^{9} + 4q^{11} + 4q^{13} + 2q^{17} + 6q^{19} + O(q^{20})$$ ## 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. 