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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 152460bh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 152460.by2 | 152460bh1 | \([0, 0, 0, -1452, -11979]\) | \(442368/175\) | \(133930011600\) | \([2]\) | \(122880\) | \(0.83345\) | \(\Gamma_0(N)\)-optimal |
| 152460.by1 | 152460bh2 | \([0, 0, 0, -10527, 407286]\) | \(10536048/245\) | \(3000032259840\) | \([2]\) | \(245760\) | \(1.1800\) |
Rank
sage: E.rank()
The elliptic curves in class 152460bh have rank \(1\).
Complex multiplication
The elliptic curves in class 152460bh do not have complex multiplication.Modular form 152460.2.a.bh
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
