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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 11025.bb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 11025.bb1 | 11025v3 | \([0, 0, 1, -1447950, -701531469]\) | \(-250523582464/13671875\) | \(-18321620086669921875\) | \([]\) | \(207360\) | \(2.4544\) | |
| 11025.bb2 | 11025v1 | \([0, 0, 1, -14700, 761031]\) | \(-262144/35\) | \(-46903347421875\) | \([]\) | \(23040\) | \(1.3558\) | \(\Gamma_0(N)\)-optimal |
| 11025.bb3 | 11025v2 | \([0, 0, 1, 95550, -1940094]\) | \(71991296/42875\) | \(-57456600591796875\) | \([]\) | \(69120\) | \(1.9051\) |
Rank
sage: E.rank()
The elliptic curves in class 11025.bb have rank \(1\).
Complex multiplication
The elliptic curves in class 11025.bb do not have complex multiplication.Modular form 11025.2.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 LMFDB numbering.
\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
