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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 23184.ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 23184.ba1 | 23184bh2 | \([0, 0, 0, -87195, 9278026]\) | \(24553362849625/1755162752\) | \(5240887894867968\) | \([2]\) | \(129024\) | \(1.7632\) | |
| 23184.ba2 | 23184bh1 | \([0, 0, 0, 4965, 633418]\) | \(4533086375/60669952\) | \(-181159505952768\) | \([2]\) | \(64512\) | \(1.4166\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 23184.ba have rank \(1\).
Complex multiplication
The elliptic curves in class 23184.ba do not have complex multiplication.Modular form 23184.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
