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SageMath
E = EllipticCurve("tc1")
E.isogeny_class()
Elliptic curves in class 436800.tc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 436800.tc1 | 436800tc1 | \([0, 1, 0, -1965633, 498700863]\) | \(820221748268836/369468094905\) | \(378335329182720000000\) | \([2]\) | \(14450688\) | \(2.6438\) | \(\Gamma_0(N)\)-optimal |
| 436800.tc2 | 436800tc2 | \([0, 1, 0, 6822367, 3741472863]\) | \(17147425715207422/12872524043925\) | \(-26362929241958400000000\) | \([2]\) | \(28901376\) | \(2.9904\) |
Rank
sage: E.rank()
The elliptic curves in class 436800.tc have rank \(1\).
Complex multiplication
The elliptic curves in class 436800.tc do not have complex multiplication.Modular form 436800.2.a.tc
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.
