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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 71148bb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 71148.ba1 | 71148bb1 | \([0, -1, 0, -102229794, 402128441541]\) | \(-35431687725461248/440311012911\) | \(-1468330708644944453265264\) | \([]\) | \(18662400\) | \(3.4477\) | \(\Gamma_0(N)\)-optimal |
| 71148.ba2 | 71148bb2 | \([0, -1, 0, 355607586, 2054731204737]\) | \(1491325446082364672/1410025768453071\) | \(-4702094826364964312340853104\) | \([]\) | \(55987200\) | \(3.9970\) |
Rank
sage: E.rank()
The elliptic curves in class 71148bb have rank \(0\).
Complex multiplication
The elliptic curves in class 71148bb do not have complex multiplication.Modular form 71148.2.a.bb
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
