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SageMath
E = EllipticCurve("ca1")
E.isogeny_class()
Elliptic curves in class 155526ca
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 155526.z1 | 155526ca1 | \([1, 0, 1, -8445232, 9445674410]\) | \(1311889499494111/438012\) | \(22240633063745124\) | \([2]\) | \(4055040\) | \(2.4947\) | \(\Gamma_0(N)\)-optimal |
| 155526.z2 | 155526ca2 | \([1, 0, 1, -8408202, 9532620850]\) | \(-1294708239486271/23981814018\) | \(-1217708021189641156686\) | \([2]\) | \(8110080\) | \(2.8413\) |
Rank
sage: E.rank()
The elliptic curves in class 155526ca have rank \(0\).
Complex multiplication
The elliptic curves in class 155526ca do not have complex multiplication.Modular form 155526.2.a.ca
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
