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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 6384c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 6384.f4 | 6384c1 | \([0, -1, 0, 41, -86]\) | \(464857088/410571\) | \(-6569136\) | \([2]\) | \(1024\) | \(-0.0043898\) | \(\Gamma_0(N)\)-optimal |
| 6384.f3 | 6384c2 | \([0, -1, 0, -204, -576]\) | \(3685542352/1432809\) | \(366799104\) | \([2, 2]\) | \(2048\) | \(0.34218\) | |
| 6384.f1 | 6384c3 | \([0, -1, 0, -2864, -58032]\) | \(2538016415428/872613\) | \(893555712\) | \([2]\) | \(4096\) | \(0.68876\) | |
| 6384.f2 | 6384c4 | \([0, -1, 0, -1464, 21600]\) | \(339112345828/8210223\) | \(8407268352\) | \([4]\) | \(4096\) | \(0.68876\) |
Rank
sage: E.rank()
The elliptic curves in class 6384c have rank \(0\).
Complex multiplication
The elliptic curves in class 6384c do not have complex multiplication.Modular form 6384.2.a.c
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
