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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 111573bh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 111573.u2 | 111573bh1 | \([1, -1, 1, -1344188, -599509466]\) | \(-1074191725926252207/4097152081\) | \(-1024480586397807\) | \([2]\) | \(2555904\) | \(2.0944\) | \(\Gamma_0(N)\)-optimal |
| 111573.u1 | 111573bh2 | \([1, -1, 1, -21507023, -38384662256]\) | \(4399901392374538640127/64009\) | \(16005258423\) | \([2]\) | \(5111808\) | \(2.4410\) |
Rank
sage: E.rank()
The elliptic curves in class 111573bh have rank \(0\).
Complex multiplication
The elliptic curves in class 111573bh do not have complex multiplication.Modular form 111573.2.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.
