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SageMath
E = EllipticCurve("cz1")
E.isogeny_class()
Elliptic curves in class 115920cz
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 115920.q4 | 115920cz1 | \([0, 0, 0, 41526717, 187202684482]\) | \(2652277923951208297919/6605028468326400000\) | \(-19722509325967137177600000\) | \([2]\) | \(29491200\) | \(3.5375\) | \(\Gamma_0(N)\)-optimal |
| 115920.q3 | 115920cz2 | \([0, 0, 0, -348494403, 2091207788098]\) | \(1567558142704512417614401/274462175610000000000\) | \(819539664976650240000000000\) | \([2, 2]\) | \(58982400\) | \(3.8841\) | |
| 115920.q2 | 115920cz3 | \([0, 0, 0, -1620832323, -23161900780478]\) | \(157706830105239346386477121/13650704956054687500000\) | \(40760786587500000000000000000\) | \([2]\) | \(117964800\) | \(4.2306\) | |
| 115920.q1 | 115920cz4 | \([0, 0, 0, -5316494403, 149200642988098]\) | \(5565604209893236690185614401/229307220930246900000\) | \(684707692782182359449600000\) | \([2]\) | \(117964800\) | \(4.2306\) |
Rank
sage: E.rank()
The elliptic curves in class 115920cz have rank \(0\).
Complex multiplication
The elliptic curves in class 115920cz do not have complex multiplication.Modular form 115920.2.a.cz
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.
