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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 377520.w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 377520.w1 | 377520w3 | \([0, -1, 0, -51117216, 140686194816]\) | \(2035678735521204409/141376950\) | \(1025875521204019200\) | \([4]\) | \(17694720\) | \(2.9101\) | |
| 377520.w2 | 377520w4 | \([0, -1, 0, -5466336, -1309368960]\) | \(2489411558640889/1338278906250\) | \(9710971770614400000000\) | \([2]\) | \(17694720\) | \(2.9101\) | |
| 377520.w3 | 377520w2 | \([0, -1, 0, -3201216, 2189788416]\) | \(499980107400409/4140922500\) | \(30047833313372160000\) | \([2, 2]\) | \(8847360\) | \(2.5635\) | |
| 377520.w4 | 377520w1 | \([0, -1, 0, -64896, 79672320]\) | \(-4165509529/375289200\) | \(-2723216221967155200\) | \([2]\) | \(4423680\) | \(2.2170\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 377520.w have rank \(0\).
Complex multiplication
The elliptic curves in class 377520.w do not have complex multiplication.Modular form 377520.2.a.w
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
