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SageMath
E = EllipticCurve("cr1")
E.isogeny_class()
Elliptic curves in class 29400cr
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 29400.bl4 | 29400cr1 | \([0, -1, 0, -8983, -2123288]\) | \(-2725888/64827\) | \(-1906707930750000\) | \([2]\) | \(147456\) | \(1.6127\) | \(\Gamma_0(N)\)-optimal |
| 29400.bl3 | 29400cr2 | \([0, -1, 0, -309108, -65749788]\) | \(6940769488/35721\) | \(16810159716000000\) | \([2, 2]\) | \(294912\) | \(1.9593\) | |
| 29400.bl2 | 29400cr3 | \([0, -1, 0, -480608, 15541212]\) | \(6522128932/3720087\) | \(7002632247408000000\) | \([2]\) | \(589824\) | \(2.3059\) | |
| 29400.bl1 | 29400cr4 | \([0, -1, 0, -4939608, -4223938788]\) | \(7080974546692/189\) | \(355770576000000\) | \([2]\) | \(589824\) | \(2.3059\) |
Rank
sage: E.rank()
The elliptic curves in class 29400cr have rank \(1\).
Complex multiplication
The elliptic curves in class 29400cr do not have complex multiplication.Modular form 29400.2.a.cr
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.
