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SageMath
E = EllipticCurve("ix1")
E.isogeny_class()
Elliptic curves in class 270480ix
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 270480.ix1 | 270480ix1 | \([0, 1, 0, -18440, 525300]\) | \(1439069689/579600\) | \(279303620198400\) | \([2]\) | \(884736\) | \(1.4699\) | \(\Gamma_0(N)\)-optimal |
| 270480.ix2 | 270480ix2 | \([0, 1, 0, 59960, 3880820]\) | \(49471280711/41992020\) | \(-20235547283374080\) | \([2]\) | \(1769472\) | \(1.8165\) |
Rank
sage: E.rank()
The elliptic curves in class 270480ix have rank \(0\).
Complex multiplication
The elliptic curves in class 270480ix do not have complex multiplication.Modular form 270480.2.a.ix
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.
