Show commands:
SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 2960j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2960.j1 | 2960j1 | \([0, -1, 0, -856, -9360]\) | \(-16954786009/370\) | \(-1515520\) | \([]\) | \(864\) | \(0.30193\) | \(\Gamma_0(N)\)-optimal |
| 2960.j2 | 2960j2 | \([0, -1, 0, -296, -21904]\) | \(-702595369/50653000\) | \(-207474688000\) | \([]\) | \(2592\) | \(0.85124\) | |
| 2960.j3 | 2960j3 | \([0, -1, 0, 2664, 589040]\) | \(510273943271/37000000000\) | \(-151552000000000\) | \([]\) | \(7776\) | \(1.4005\) |
Rank
sage: E.rank()
The elliptic curves in class 2960j have rank \(1\).
Complex multiplication
The elliptic curves in class 2960j do not have complex multiplication.Modular form 2960.2.a.j
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
