# Properties

 Label 3850.t Number of curves $4$ Conductor $3850$ CM no Rank $1$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 3850.t

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3850.t1 3850s3 $$[1, -1, 1, -81666730, -284043362603]$$ $$3855131356812007128171561/8967612500$$ $$140118945312500$$ $$$$ $$245760$$ $$2.8447$$
3850.t2 3850s4 $$[1, -1, 1, -5373730, -3942310603]$$ $$1098325674097093229481/205612182617187500$$ $$3212690353393554687500$$ $$$$ $$245760$$ $$2.8447$$
3850.t3 3850s2 $$[1, -1, 1, -5104230, -4437112603]$$ $$941226862950447171561/45393906250000$$ $$709279785156250000$$ $$[2, 2]$$ $$122880$$ $$2.4982$$
3850.t4 3850s1 $$[1, -1, 1, -302230, -76896603]$$ $$-195395722614328041/50730248800000$$ $$-792660137500000000$$ $$$$ $$61440$$ $$2.1516$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 3850.t have rank $$1$$.

## Complex multiplication

The elliptic curves in class 3850.t do not have complex multiplication.

## Modular form3850.2.a.t

sage: E.q_eigenform(10)

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