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SageMath
E = EllipticCurve("tz1")
E.isogeny_class()
Elliptic curves in class 369600tz
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 369600.tz4 | 369600tz1 | \([0, 1, 0, 2767, -2216337]\) | \(9148592/8301447\) | \(-2125170432000000\) | \([2]\) | \(2097152\) | \(1.6201\) | \(\Gamma_0(N)\)-optimal |
| 369600.tz3 | 369600tz2 | \([0, 1, 0, -239233, -44082337]\) | \(1478729816932/38900169\) | \(39833773056000000\) | \([2, 2]\) | \(4194304\) | \(1.9666\) | |
| 369600.tz2 | 369600tz3 | \([0, 1, 0, -547233, 92361663]\) | \(8849350367426/3314597517\) | \(6788295714816000000\) | \([2]\) | \(8388608\) | \(2.3132\) | |
| 369600.tz1 | 369600tz4 | \([0, 1, 0, -3803233, -2856078337]\) | \(2970658109581346/2139291\) | \(4381267968000000\) | \([2]\) | \(8388608\) | \(2.3132\) |
Rank
sage: E.rank()
The elliptic curves in class 369600tz have rank \(1\).
Complex multiplication
The elliptic curves in class 369600tz do not have complex multiplication.Modular form 369600.2.a.tz
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.
