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SageMath
E = EllipticCurve("cx1")
E.isogeny_class()
Elliptic curves in class 229320.cx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 229320.cx1 | 229320d1 | \([0, 0, 0, -8022, -55811]\) | \(14270199808/7921875\) | \(31693457250000\) | \([2]\) | \(442368\) | \(1.2810\) | \(\Gamma_0(N)\)-optimal |
| 229320.cx2 | 229320d2 | \([0, 0, 0, 31353, -441686]\) | \(53247522512/32131125\) | \(-2056778601696000\) | \([2]\) | \(884736\) | \(1.6276\) |
Rank
sage: E.rank()
The elliptic curves in class 229320.cx have rank \(2\).
Complex multiplication
The elliptic curves in class 229320.cx do not have complex multiplication.Modular form 229320.2.a.cx
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
