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SageMath
E = EllipticCurve("cz1")
E.isogeny_class()
Elliptic curves in class 37440.cz
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 37440.cz1 | 37440cl3 | \([0, 0, 0, -119532, 15268016]\) | \(988345570681/44994560\) | \(8598594319810560\) | \([2]\) | \(331776\) | \(1.8195\) | |
| 37440.cz2 | 37440cl1 | \([0, 0, 0, -18732, -980944]\) | \(3803721481/26000\) | \(4968677376000\) | \([2]\) | \(110592\) | \(1.2702\) | \(\Gamma_0(N)\)-optimal |
| 37440.cz3 | 37440cl2 | \([0, 0, 0, -7212, -2174416]\) | \(-217081801/10562500\) | \(-2018525184000000\) | \([2]\) | \(221184\) | \(1.6167\) | |
| 37440.cz4 | 37440cl4 | \([0, 0, 0, 64788, 58103984]\) | \(157376536199/7722894400\) | \(-1475868103173734400\) | \([2]\) | \(663552\) | \(2.1660\) |
Rank
sage: E.rank()
The elliptic curves in class 37440.cz have rank \(1\).
Complex multiplication
The elliptic curves in class 37440.cz do not have complex multiplication.Modular form 37440.2.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 LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
