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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 327990.ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 327990.ba1 | 327990ba3 | \([1, 1, 1, -72770486, 238905369683]\) | \(71647584155243142409/10140000\) | \(6031508474940000\) | \([2]\) | \(32112640\) | \(2.8809\) | |
| 327990.ba2 | 327990ba4 | \([1, 1, 1, -5221366, 2553636179]\) | \(26465989780414729/10571870144160\) | \(6288394908329999955360\) | \([2]\) | \(32112640\) | \(2.8809\) | |
| 327990.ba3 | 327990ba2 | \([1, 1, 1, -4548566, 3730767059]\) | \(17496824387403529/6580454400\) | \(3914207739897062400\) | \([2, 2]\) | \(16056320\) | \(2.5343\) | |
| 327990.ba4 | 327990ba1 | \([1, 1, 1, -242646, 75902163]\) | \(-2656166199049/2658140160\) | \(-1581123757654671360\) | \([2]\) | \(8028160\) | \(2.1878\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 327990.ba have rank \(0\).
Complex multiplication
The elliptic curves in class 327990.ba do not have complex multiplication.Modular form 327990.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
