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SageMath
E = EllipticCurve("dz1")
E.isogeny_class()
Elliptic curves in class 377520dz
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 377520.dz3 | 377520dz1 | \([0, 1, 0, -127816, -12761740]\) | \(31824875809/8785920\) | \(63753393033707520\) | \([2]\) | \(3317760\) | \(1.9320\) | \(\Gamma_0(N)\)-optimal |
| 377520.dz2 | 377520dz2 | \([0, 1, 0, -747336, 238267764]\) | \(6361447449889/294465600\) | \(2136734813395353600\) | \([2, 2]\) | \(6635520\) | \(2.2785\) | |
| 377520.dz1 | 377520dz3 | \([0, 1, 0, -11821256, 15639875700]\) | \(25176685646263969/57915000\) | \(420249416970240000\) | \([2]\) | \(13271040\) | \(2.6251\) | |
| 377520.dz4 | 377520dz4 | \([0, 1, 0, 414264, 912460404]\) | \(1083523132511/50179392120\) | \(-364117418326013214720\) | \([2]\) | \(13271040\) | \(2.6251\) |
Rank
sage: E.rank()
The elliptic curves in class 377520dz have rank \(1\).
Complex multiplication
The elliptic curves in class 377520dz do not have complex multiplication.Modular form 377520.2.a.dz
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
