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SageMath
E = EllipticCurve("eu1")
E.isogeny_class()
Elliptic curves in class 377520eu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 377520.eu4 | 377520eu1 | \([0, 1, 0, 10124, 280124]\) | \(253012016/219375\) | \(-99490865760000\) | \([2]\) | \(983040\) | \(1.3735\) | \(\Gamma_0(N)\)-optimal |
| 377520.eu3 | 377520eu2 | \([0, 1, 0, -50376, 2433924]\) | \(7793764996/3080025\) | \(5587407021081600\) | \([2, 2]\) | \(1966080\) | \(1.7200\) | |
| 377520.eu1 | 377520eu3 | \([0, 1, 0, -703776, 226942164]\) | \(10625310339698/3855735\) | \(13989211652782080\) | \([2]\) | \(3932160\) | \(2.0666\) | |
| 377520.eu2 | 377520eu4 | \([0, 1, 0, -364976, -83263116]\) | \(1481943889298/34543665\) | \(125329837488261120\) | \([2]\) | \(3932160\) | \(2.0666\) |
Rank
sage: E.rank()
The elliptic curves in class 377520eu have rank \(1\).
Complex multiplication
The elliptic curves in class 377520eu do not have complex multiplication.Modular form 377520.2.a.eu
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.
