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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 43320.bc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 43320.bc1 | 43320be4 | \([0, 1, 0, -10974520, -13997160832]\) | \(3034301922374404/1425\) | \(68649349555200\) | \([2]\) | \(737280\) | \(2.4287\) | |
| 43320.bc2 | 43320be3 | \([0, 1, 0, -823200, -125190000]\) | \(1280615525284/601171875\) | \(28961444343600000000\) | \([4]\) | \(737280\) | \(2.4287\) | |
| 43320.bc3 | 43320be2 | \([0, 1, 0, -686020, -218801632]\) | \(2964647793616/2030625\) | \(24456330779040000\) | \([2, 2]\) | \(368640\) | \(2.0821\) | |
| 43320.bc4 | 43320be1 | \([0, 1, 0, -34415, -4814550]\) | \(-5988775936/9774075\) | \(-7357279509361200\) | \([2]\) | \(184320\) | \(1.7355\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 43320.bc have rank \(1\).
Complex multiplication
The elliptic curves in class 43320.bc do not have complex multiplication.Modular form 43320.2.a.bc
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
