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SageMath
E = EllipticCurve("cp1")
E.isogeny_class()
Elliptic curves in class 73152cp
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 73152.bf2 | 73152cp1 | \([0, 0, 0, -58720908, 171561196816]\) | \(117174888570509216929/1273887851544576\) | \(243443759520414670258176\) | \([]\) | \(5677056\) | \(3.3025\) | \(\Gamma_0(N)\)-optimal |
| 73152.bf1 | 73152cp2 | \([0, 0, 0, -12879997068, -562628526647024]\) | \(1236526859255318155975783969/38367061931916216\) | \(7332059715565498260258816\) | \([]\) | \(39739392\) | \(4.2755\) |
Rank
sage: E.rank()
The elliptic curves in class 73152cp have rank \(1\).
Complex multiplication
The elliptic curves in class 73152cp do not have complex multiplication.Modular form 73152.2.a.cp
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
