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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 323400.bh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 323400.bh1 | 323400bh2 | \([0, -1, 0, -2739183708, 55180678943412]\) | \(112650941975539952/11979\) | \(241697929126500000000\) | \([2]\) | \(104939520\) | \(3.7831\) | |
| 323400.bh2 | 323400bh1 | \([0, -1, 0, -171185583, 862382603412]\) | \(-439939433818112/143496441\) | \(-180956218312896468750000\) | \([2]\) | \(52469760\) | \(3.4366\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 323400.bh have rank \(1\).
Complex multiplication
The elliptic curves in class 323400.bh do not have complex multiplication.Modular form 323400.2.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 LMFDB 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 LMFDB labels.
