# Properties

 Label 10080t Number of curves $4$ Conductor $10080$ CM no Rank $1$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 10080t

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10080.z3 10080t1 $$[0, 0, 0, -57408753, -167423033752]$$ $$448487713888272974160064/91549016015625$$ $$4271310891225000000$$ $$[2, 2]$$ $$860160$$ $$2.9627$$ $$\Gamma_0(N)$$-optimal
10080.z1 10080t2 $$[0, 0, 0, -918540003, -10715075262502]$$ $$229625675762164624948320008/9568125$$ $$3571283520000$$ $$$$ $$1720320$$ $$3.3093$$
10080.z2 10080t3 $$[0, 0, 0, -57605628, -166216898752]$$ $$7079962908642659949376/100085966990454375$$ $$298855096058024916480000$$ $$$$ $$1720320$$ $$3.3093$$
10080.z4 10080t4 $$[0, 0, 0, -57211923, -168628066378]$$ $$-55486311952875723077768/801237030029296875$$ $$-299060118984375000000000$$ $$$$ $$1720320$$ $$3.3093$$

## Rank

sage: E.rank()

The elliptic curves in class 10080t have rank $$1$$.

## Complex multiplication

The elliptic curves in class 10080t do not have complex multiplication.

## Modular form 10080.2.a.t

sage: E.q_eigenform(10)

$$q - q^{5} + q^{7} + 4q^{11} - 6q^{13} - 6q^{17} - 4q^{19} + O(q^{20})$$ ## 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 Cremona numbering.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 