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SageMath
E = EllipticCurve("bk1")
E.isogeny_class()
Elliptic curves in class 102312bk
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 102312.bb2 | 102312bk1 | \([0, 0, 0, -938595, 414509326]\) | \(-1041220466500/242597383\) | \(-21305995780773215232\) | \([2]\) | \(1769472\) | \(2.4282\) | \(\Gamma_0(N)\)-optimal |
| 102312.bb1 | 102312bk2 | \([0, 0, 0, -15773835, 24112321702]\) | \(2471097448795250/98942809\) | \(17379207022128924672\) | \([2]\) | \(3538944\) | \(2.7747\) |
Rank
sage: E.rank()
The elliptic curves in class 102312bk have rank \(1\).
Complex multiplication
The elliptic curves in class 102312bk do not have complex multiplication.Modular form 102312.2.a.bk
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.
