# Properties

 Label 770.c Number of curves $4$ Conductor $770$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 770.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
770.c1 770c3 $$[1, -1, 0, -3266669, -2271693567]$$ $$3855131356812007128171561/8967612500$$ $$8967612500$$ $$$$ $$10240$$ $$2.0400$$
770.c2 770c4 $$[1, -1, 0, -214949, -31495495]$$ $$1098325674097093229481/205612182617187500$$ $$205612182617187500$$ $$$$ $$10240$$ $$2.0400$$
770.c3 770c2 $$[1, -1, 0, -204169, -35456067]$$ $$941226862950447171561/45393906250000$$ $$45393906250000$$ $$[2, 2]$$ $$5120$$ $$1.6934$$
770.c4 770c1 $$[1, -1, 0, -12089, -612755]$$ $$-195395722614328041/50730248800000$$ $$-50730248800000$$ $$$$ $$2560$$ $$1.3469$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 770.c have rank $$0$$.

## Complex multiplication

The elliptic curves in class 770.c do not have complex multiplication.

## Modular form770.2.a.c

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} + q^{5} - q^{7} - q^{8} - 3 q^{9} - q^{10} - q^{11} + 2 q^{13} + q^{14} + q^{16} + 6 q^{17} + 3 q^{18} + 4 q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 