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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 109330ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 109330.ba2 | 109330ba1 | \([1, 1, 1, -27350, 1719235]\) | \(3803721481/26000\) | \(15465406346000\) | \([2]\) | \(580608\) | \(1.3648\) | \(\Gamma_0(N)\)-optimal |
| 109330.ba3 | 109330ba2 | \([1, 1, 1, -10530, 3831827]\) | \(-217081801/10562500\) | \(-6282821328062500\) | \([2]\) | \(1161216\) | \(1.7114\) | |
| 109330.ba1 | 109330ba3 | \([1, 1, 1, -174525, -27009325]\) | \(988345570681/44994560\) | \(26763813606133760\) | \([2]\) | \(1741824\) | \(1.9141\) | |
| 109330.ba4 | 109330ba4 | \([1, 1, 1, 94595, -102470573]\) | \(157376536199/7722894400\) | \(-4593757694740302400\) | \([2]\) | \(3483648\) | \(2.2607\) |
Rank
sage: E.rank()
The elliptic curves in class 109330ba have rank \(0\).
Complex multiplication
The elliptic curves in class 109330ba do not have complex multiplication.Modular form 109330.2.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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
