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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 11400.a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 11400.a1 | 11400bb3 | \([0, -1, 0, -821008, -286057988]\) | \(3825131988299044/961875\) | \(15390000000000\) | \([2]\) | \(122880\) | \(1.9056\) | |
| 11400.a2 | 11400bb2 | \([0, -1, 0, -51508, -4420988]\) | \(3778298043856/59213025\) | \(236852100000000\) | \([2, 2]\) | \(61440\) | \(1.5590\) | |
| 11400.a3 | 11400bb1 | \([0, -1, 0, -6383, 91512]\) | \(115060504576/52780005\) | \(13195001250000\) | \([4]\) | \(30720\) | \(1.2124\) | \(\Gamma_0(N)\)-optimal |
| 11400.a4 | 11400bb4 | \([0, -1, 0, -4008, -12305988]\) | \(-445138564/4089438495\) | \(-65431015920000000\) | \([2]\) | \(122880\) | \(1.9056\) |
Rank
sage: E.rank()
The elliptic curves in class 11400.a have rank \(1\).
Complex multiplication
The elliptic curves in class 11400.a do not have complex multiplication.Modular form 11400.2.a.a
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
