Show commands:
SageMath
E = EllipticCurve("dn1")
E.isogeny_class()
Elliptic curves in class 46800dn
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
46800.f2 | 46800dn1 | \([0, 0, 0, -480, 3760]\) | \(163840/13\) | \(970444800\) | \([]\) | \(25920\) | \(0.46803\) | \(\Gamma_0(N)\)-optimal |
46800.f1 | 46800dn2 | \([0, 0, 0, -7680, -258320]\) | \(671088640/2197\) | \(164005171200\) | \([]\) | \(77760\) | \(1.0173\) |
Rank
sage: E.rank()
The elliptic curves in class 46800dn have rank \(1\).
Complex multiplication
The elliptic curves in class 46800dn do not have complex multiplication.Modular form 46800.2.a.dn
sage: E.q_eigenform(10)
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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.