Properties

 Label 3120.r Number of curves $4$ Conductor $3120$ CM no Rank $1$ Graph

Related objects

Show commands: SageMath
E = EllipticCurve("r1")

E.isogeny_class()

Elliptic curves in class 3120.r

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3120.r1 3120g3 $$[0, 1, 0, -7696, -261820]$$ $$49235161015876/137109375$$ $$140400000000$$ $$[2]$$ $$3072$$ $$1.0115$$
3120.r2 3120g4 $$[0, 1, 0, -7176, 230724]$$ $$39914580075556/172718325$$ $$176863564800$$ $$[4]$$ $$3072$$ $$1.0115$$
3120.r3 3120g2 $$[0, 1, 0, -676, -676]$$ $$133649126224/77000625$$ $$19712160000$$ $$[2, 2]$$ $$1536$$ $$0.66494$$
3120.r4 3120g1 $$[0, 1, 0, 169, 0]$$ $$33165879296/19278675$$ $$-308458800$$ $$[2]$$ $$768$$ $$0.31837$$ $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 3120.r have rank $$1$$.

Complex multiplication

The elliptic curves in class 3120.r do not have complex multiplication.

Modular form3120.2.a.r

sage: E.q_eigenform(10)

$$q + q^{3} - q^{5} + q^{9} + q^{13} - q^{15} - 6 q^{17} - 4 q^{19} + O(q^{20})$$

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.