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SageMath
E = EllipticCurve("cj1")
E.isogeny_class()
Elliptic curves in class 60984.cj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 60984.cj1 | 60984bc2 | \([0, 0, 0, -43923, -3500530]\) | \(3543122/49\) | \(129601393625088\) | \([2]\) | \(276480\) | \(1.5136\) | |
| 60984.cj2 | 60984bc1 | \([0, 0, 0, -363, -146410]\) | \(-4/7\) | \(-9257242401792\) | \([2]\) | \(138240\) | \(1.1670\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 60984.cj have rank \(1\).
Complex multiplication
The elliptic curves in class 60984.cj do not have complex multiplication.Modular form 60984.2.a.cj
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 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.
