Show commands:
SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 13328u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
13328.w2 | 13328u1 | \([0, -1, 0, -14128, -638784]\) | \(647214625/3332\) | \(1605658492928\) | \([2]\) | \(18432\) | \(1.1879\) | \(\Gamma_0(N)\)-optimal |
13328.w1 | 13328u2 | \([0, -1, 0, -21968, 157760]\) | \(2433138625/1387778\) | \(668756762304512\) | \([2]\) | \(36864\) | \(1.5345\) |
Rank
sage: E.rank()
The elliptic curves in class 13328u have rank \(0\).
Complex multiplication
The elliptic curves in class 13328u do not have complex multiplication.Modular form 13328.2.a.u
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.