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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 179088ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 179088.c2 | 179088ba1 | \([0, -1, 0, -4919712, -2655426816]\) | \(3215014175651328584353/1115930860975816704\) | \(4570852806556945219584\) | \([]\) | \(10450944\) | \(2.8578\) | \(\Gamma_0(N)\)-optimal |
| 179088.c1 | 179088ba2 | \([0, -1, 0, -164863392, 814699190016]\) | \(120986373702456846135875233/21429653098766238144\) | \(87775859092546511437824\) | \([]\) | \(31352832\) | \(3.4071\) |
Rank
sage: E.rank()
The elliptic curves in class 179088ba have rank \(1\).
Complex multiplication
The elliptic curves in class 179088ba do not have complex multiplication.Modular form 179088.2.a.ba
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
