# Properties

 Label 102960.eq Number of curves $4$ Conductor $102960$ CM no Rank $0$ Graph

# Learn more

Show commands: SageMath
sage: E = EllipticCurve("eq1")

sage: E.isogeny_class()

## Elliptic curves in class 102960.eq

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
102960.eq1 102960bi4 $$[0, 0, 0, -230947707, 1350885672394]$$ $$912446049969377120252018/17177299425$$ $$25645570623129600$$ $$[4]$$ $$11010048$$ $$3.1367$$
102960.eq2 102960bi3 $$[0, 0, 0, -15721707, 17118745594]$$ $$287849398425814280018/81784533026485575$$ $$122103653532278751590400$$ $$[2]$$ $$11010048$$ $$3.1367$$
102960.eq3 102960bi2 $$[0, 0, 0, -14434707, 21106128994]$$ $$445574312599094932036/61129333175625$$ $$45632802698271360000$$ $$[2, 2]$$ $$5505024$$ $$2.7901$$
102960.eq4 102960bi1 $$[0, 0, 0, -822207, 390626494]$$ $$-329381898333928144/162600887109375$$ $$-30345227955900000000$$ $$[2]$$ $$2752512$$ $$2.4435$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 102960.eq have rank $$0$$.

## Complex multiplication

The elliptic curves in class 102960.eq do not have complex multiplication.

## Modular form 102960.2.a.eq

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.