Show commands:
SageMath
E = EllipticCurve("dn1")
E.isogeny_class()
Elliptic curves in class 308550dn
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
308550.dn2 | 308550dn1 | \([1, 0, 1, -800176, 13551998]\) | \(2046931732873/1181672448\) | \(32709450369552000000\) | \([2]\) | \(7372800\) | \(2.4340\) | \(\Gamma_0(N)\)-optimal |
308550.dn1 | 308550dn2 | \([1, 0, 1, -9028176, 10413743998]\) | \(2940001530995593/8673562656\) | \(240089770819156500000\) | \([2]\) | \(14745600\) | \(2.7806\) |
Rank
sage: E.rank()
The elliptic curves in class 308550dn have rank \(1\).
Complex multiplication
The elliptic curves in class 308550dn do not have complex multiplication.Modular form 308550.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.