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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 123210.j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 123210.j1 | 123210ba1 | \([1, -1, 0, -659430, -205950114]\) | \(-16954786009/370\) | \(-692053384299570\) | \([]\) | \(1181952\) | \(1.9636\) | \(\Gamma_0(N)\)-optimal |
| 123210.j2 | 123210ba2 | \([1, -1, 0, -228195, -470124675]\) | \(-702595369/50653000\) | \(-94742108310611133000\) | \([]\) | \(3545856\) | \(2.5129\) | |
| 123210.j3 | 123210ba3 | \([1, -1, 0, 2051190, 12605795316]\) | \(510273943271/37000000000\) | \(-69205338429957000000000\) | \([]\) | \(10637568\) | \(3.0622\) |
Rank
sage: E.rank()
The elliptic curves in class 123210.j have rank \(0\).
Complex multiplication
The elliptic curves in class 123210.j do not have complex multiplication.Modular form 123210.2.a.j
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
