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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 33462.t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 33462.t1 | 33462q3 | \([1, -1, 0, -122472, 16464384]\) | \(57736239625/255552\) | \(899222005611072\) | \([2]\) | \(207360\) | \(1.7217\) | |
| 33462.t2 | 33462q4 | \([1, -1, 0, -61632, 32781672]\) | \(-7357983625/127552392\) | \(-448824183550626312\) | \([2]\) | \(414720\) | \(2.0683\) | |
| 33462.t3 | 33462q1 | \([1, -1, 0, -8397, -277263]\) | \(18609625/1188\) | \(4180267588068\) | \([2]\) | \(69120\) | \(1.1724\) | \(\Gamma_0(N)\)-optimal |
| 33462.t4 | 33462q2 | \([1, -1, 0, 6813, -1180737]\) | \(9938375/176418\) | \(-620769736828098\) | \([2]\) | \(138240\) | \(1.5190\) |
Rank
sage: E.rank()
The elliptic curves in class 33462.t have rank \(0\).
Complex multiplication
The elliptic curves in class 33462.t do not have complex multiplication.Modular form 33462.2.a.t
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
