# Properties

 Label 13860.m Number of curves $2$ Conductor $13860$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("m1")

sage: E.isogeny_class()

## Elliptic curves in class 13860.m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
13860.m1 13860p2 $$[0, 0, 0, -887575503, 10152728950502]$$ $$414354576760345737269208016/1182266314178222109375$$ $$220639268617196522940000000$$ $$$$ $$6988800$$ $$3.9263$$
13860.m2 13860p1 $$[0, 0, 0, -33278628, 286796059877]$$ $$-349439858058052607328256/2844147488104248046875$$ $$-33174136301247949218750000$$ $$$$ $$3494400$$ $$3.5798$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 13860.m have rank $$1$$.

## Complex multiplication

The elliptic curves in class 13860.m do not have complex multiplication.

## Modular form 13860.2.a.m

sage: E.q_eigenform(10)

$$q - q^{5} + q^{7} + q^{11} + 4q^{13} - 2q^{17} + 2q^{19} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 