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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 74529bg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 74529.bs2 | 74529bg1 | \([0, 0, 1, -3549, 88429]\) | \(-28672/3\) | \(-517255332867\) | \([]\) | \(112320\) | \(0.98669\) | \(\Gamma_0(N)\)-optimal |
| 74529.bs1 | 74529bg2 | \([0, 0, 1, -1387659, -629681621]\) | \(-1713910976512/1594323\) | \(-274890691354171347\) | \([]\) | \(1460160\) | \(2.2692\) |
Rank
sage: E.rank()
The elliptic curves in class 74529bg have rank \(1\).
Complex multiplication
The elliptic curves in class 74529bg do not have complex multiplication.Modular form 74529.2.a.bg
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.
\(\left(\begin{array}{rr} 1 & 13 \\ 13 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
