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SageMath
E = EllipticCurve("rc1")
E.isogeny_class()
Elliptic curves in class 369600.rc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 369600.rc1 | 369600rc2 | \([0, 1, 0, -11912033, -15824339937]\) | \(45637459887836881/13417633152\) | \(54958625390592000000\) | \([2]\) | \(20643840\) | \(2.7668\) | |
| 369600.rc2 | 369600rc1 | \([0, 1, 0, -648033, -313811937]\) | \(-7347774183121/6119866368\) | \(-25066972643328000000\) | \([2]\) | \(10321920\) | \(2.4202\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 369600.rc have rank \(0\).
Complex multiplication
The elliptic curves in class 369600.rc do not have complex multiplication.Modular form 369600.2.a.rc
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.
