# Properties

 Label 3920.t Number of curves $4$ Conductor $3920$ CM no Rank $0$ Graph # Learn more

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

sage: E.isogeny_class()

## Elliptic curves in class 3920.t

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3920.t1 3920ba3 $$[0, 0, 0, -209867, -37003526]$$ $$2121328796049/120050$$ $$57850930995200$$ $$$$ $$18432$$ $$1.7051$$
3920.t2 3920ba4 $$[0, 0, 0, -68747, 6483386]$$ $$74565301329/5468750$$ $$2635337600000000$$ $$$$ $$18432$$ $$1.7051$$
3920.t3 3920ba2 $$[0, 0, 0, -13867, -508326]$$ $$611960049/122500$$ $$59031562240000$$ $$[2, 2]$$ $$9216$$ $$1.3585$$
3920.t4 3920ba1 $$[0, 0, 0, 1813, -47334]$$ $$1367631/2800$$ $$-1349292851200$$ $$$$ $$4608$$ $$1.0119$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 3920.t have rank $$0$$.

## Complex multiplication

The elliptic curves in class 3920.t do not have complex multiplication.

## Modular form3920.2.a.t

sage: E.q_eigenform(10)

$$q + q^{5} - 3q^{9} - 4q^{11} + 6q^{13} - 2q^{17} + O(q^{20})$$ ## 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. 