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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 4560.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4560.l1 | 4560c3 | \([0, -1, 0, -32840, 2301600]\) | \(3825131988299044/961875\) | \(984960000\) | \([4]\) | \(10240\) | \(1.1008\) | |
| 4560.l2 | 4560c2 | \([0, -1, 0, -2060, 36192]\) | \(3778298043856/59213025\) | \(15158534400\) | \([2, 2]\) | \(5120\) | \(0.75427\) | |
| 4560.l3 | 4560c1 | \([0, -1, 0, -255, -630]\) | \(115060504576/52780005\) | \(844480080\) | \([2]\) | \(2560\) | \(0.40769\) | \(\Gamma_0(N)\)-optimal |
| 4560.l4 | 4560c4 | \([0, -1, 0, -160, 98512]\) | \(-445138564/4089438495\) | \(-4187585018880\) | \([2]\) | \(10240\) | \(1.1008\) |
Rank
sage: E.rank()
The elliptic curves in class 4560.l have rank \(0\).
Complex multiplication
The elliptic curves in class 4560.l do not have complex multiplication.Modular form 4560.2.a.l
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.
