# Properties

 Label 5070.t Number of curves $4$ Conductor $5070$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("t1")

sage: E.isogeny_class()

## Elliptic curves in class 5070.t

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5070.t1 5070t4 $$[1, 0, 0, -147465601, -689269402615]$$ $$73474353581350183614361/576510977802240$$ $$2782708376254652252160$$ $$[2]$$ $$725760$$ $$3.2879$$
5070.t2 5070t3 $$[1, 0, 0, -9020801, -11249839095]$$ $$-16818951115904497561/1592332281446400$$ $$-7685883787076016537600$$ $$[2]$$ $$362880$$ $$2.9413$$
5070.t3 5070t2 $$[1, 0, 0, -2704426, 64216580]$$ $$453198971846635561/261896250564000$$ $$1264123179288570276000$$ $$[2]$$ $$241920$$ $$2.7386$$
5070.t4 5070t1 $$[1, 0, 0, 675574, 8108580]$$ $$7064514799444439/4094064000000$$ $$-19761264961776000000$$ $$[2]$$ $$120960$$ $$2.3920$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 5070.t have rank $$1$$.

## Complex multiplication

The elliptic curves in class 5070.t do not have complex multiplication.

## Modular form5070.2.a.t

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} - 2 q^{7} + q^{8} + q^{9} - q^{10} + q^{12} - 2 q^{14} - q^{15} + q^{16} + q^{18} - 2 q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.