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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 35520.ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 35520.ba1 | 35520m2 | \([0, -1, 0, -453665, -117607263]\) | \(-39390416456458249/56832000000\) | \(-14898167808000000\) | \([]\) | \(414720\) | \(2.0057\) | |
| 35520.ba2 | 35520m1 | \([0, -1, 0, 8095, -767775]\) | \(223759095911/1094104800\) | \(-286813008691200\) | \([]\) | \(138240\) | \(1.4564\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 35520.ba have rank \(0\).
Complex multiplication
The elliptic curves in class 35520.ba do not have complex multiplication.Modular form 35520.2.a.ba
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
