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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 390225.bc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 390225.bc1 | 390225bc4 | \([1, 1, 0, -739675, -242155250]\) | \(1616855892553/22851963\) | \(632556975378796875\) | \([2]\) | \(5529600\) | \(2.2205\) | |
| 390225.bc2 | 390225bc2 | \([1, 1, 0, -89300, 4336875]\) | \(2845178713/1347921\) | \(37311316791890625\) | \([2, 2]\) | \(2764800\) | \(1.8739\) | |
| 390225.bc3 | 390225bc1 | \([1, 1, 0, -74175, 7740000]\) | \(1630532233/1161\) | \(32137223765625\) | \([2]\) | \(1382400\) | \(1.5273\) | \(\Gamma_0(N)\)-optimal |
| 390225.bc4 | 390225bc3 | \([1, 1, 0, 319075, 33331500]\) | \(129784785047/92307627\) | \(-2555134249933546875\) | \([2]\) | \(5529600\) | \(2.2205\) |
Rank
sage: E.rank()
The elliptic curves in class 390225.bc have rank \(0\).
Complex multiplication
The elliptic curves in class 390225.bc do not have complex multiplication.Modular form 390225.2.a.bc
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.
