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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 4368.x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4368.x1 | 4368f3 | \([0, 1, 0, -952, 10868]\) | \(46640233586/599781\) | \(1228351488\) | \([2]\) | \(2560\) | \(0.55255\) | |
| 4368.x2 | 4368f2 | \([0, 1, 0, -112, -220]\) | \(153091012/74529\) | \(76317696\) | \([2, 2]\) | \(1280\) | \(0.20598\) | |
| 4368.x3 | 4368f1 | \([0, 1, 0, -92, -372]\) | \(340062928/273\) | \(69888\) | \([2]\) | \(640\) | \(-0.14060\) | \(\Gamma_0(N)\)-optimal |
| 4368.x4 | 4368f4 | \([0, 1, 0, 408, -1260]\) | \(3658553134/2528253\) | \(-5177862144\) | \([2]\) | \(2560\) | \(0.55255\) |
Rank
sage: E.rank()
The elliptic curves in class 4368.x have rank \(0\).
Complex multiplication
The elliptic curves in class 4368.x do not have complex multiplication.Modular form 4368.2.a.x
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.
