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SageMath
E = EllipticCurve("cb1")
E.isogeny_class()
Elliptic curves in class 33150cb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 33150.ck3 | 33150cb1 | \([1, 0, 0, -5213, 144417]\) | \(1002702430729/159120\) | \(2486250000\) | \([2]\) | \(49152\) | \(0.81315\) | \(\Gamma_0(N)\)-optimal |
| 33150.ck2 | 33150cb2 | \([1, 0, 0, -5713, 114917]\) | \(1319778683209/395612100\) | \(6181439062500\) | \([2, 2]\) | \(98304\) | \(1.1597\) | |
| 33150.ck4 | 33150cb3 | \([1, 0, 0, 15537, 773667]\) | \(26546265663191/31856082570\) | \(-497751290156250\) | \([2]\) | \(196608\) | \(1.5063\) | |
| 33150.ck1 | 33150cb4 | \([1, 0, 0, -34963, -2429833]\) | \(302503589987689/12214946250\) | \(190858535156250\) | \([2]\) | \(196608\) | \(1.5063\) |
Rank
sage: E.rank()
The elliptic curves in class 33150cb have rank \(0\).
Complex multiplication
The elliptic curves in class 33150cb do not have complex multiplication.Modular form 33150.2.a.cb
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
