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SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 254800.bf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 254800.bf1 | 254800bf1 | \([0, 1, 0, -4405508, 3553608988]\) | \(20093868785104/26374985\) | \(12411962441060000000\) | \([2]\) | \(8847360\) | \(2.5705\) | \(\Gamma_0(N)\)-optimal |
| 254800.bf2 | 254800bf2 | \([0, 1, 0, -3205008, 5534433988]\) | \(-1934207124196/5912841025\) | \(-11130237340003600000000\) | \([2]\) | \(17694720\) | \(2.9170\) |
Rank
sage: E.rank()
The elliptic curves in class 254800.bf have rank \(0\).
Complex multiplication
The elliptic curves in class 254800.bf do not have complex multiplication.Modular form 254800.2.a.bf
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.
