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SageMath
E = EllipticCurve("mf1")
E.isogeny_class()
Elliptic curves in class 100800mf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 100800.bk3 | 100800mf1 | \([0, 0, 0, -8175, -142000]\) | \(82881856/36015\) | \(26254935000000\) | \([2]\) | \(294912\) | \(1.2710\) | \(\Gamma_0(N)\)-optimal |
| 100800.bk2 | 100800mf2 | \([0, 0, 0, -63300, 6032000]\) | \(601211584/11025\) | \(514382400000000\) | \([2, 2]\) | \(589824\) | \(1.6176\) | |
| 100800.bk4 | 100800mf3 | \([0, 0, 0, -300, 17498000]\) | \(-8/354375\) | \(-132269760000000000\) | \([2]\) | \(1179648\) | \(1.9642\) | |
| 100800.bk1 | 100800mf4 | \([0, 0, 0, -1008300, 389702000]\) | \(303735479048/105\) | \(39191040000000\) | \([2]\) | \(1179648\) | \(1.9642\) |
Rank
sage: E.rank()
The elliptic curves in class 100800mf have rank \(1\).
Complex multiplication
The elliptic curves in class 100800mf do not have complex multiplication.Modular form 100800.2.a.mf
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.
