Properties

 Label 107712.dn Number of curves $2$ Conductor $107712$ CM no Rank $2$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("dn1")

sage: E.isogeny_class()

Elliptic curves in class 107712.dn

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
107712.dn1 107712x2 [0, 0, 0, -104844, -13066000] [2] 294912
107712.dn2 107712x1 [0, 0, 0, -6924, -179728] [2] 147456 $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 107712.dn have rank $$2$$.

Complex multiplication

The elliptic curves in class 107712.dn do not have complex multiplication.

Modular form 107712.2.a.dn

sage: E.q_eigenform(10)

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

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.