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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 57154n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 57154.o4 | 57154n1 | \([1, 1, 1, -5078, 84115]\) | \(3048625/1088\) | \(5168113414208\) | \([2]\) | \(138240\) | \(1.1404\) | \(\Gamma_0(N)\)-optimal |
| 57154.o3 | 57154n2 | \([1, 1, 1, -72318, 7453619]\) | \(8805624625/2312\) | \(10982241005192\) | \([2]\) | \(276480\) | \(1.4870\) | |
| 57154.o2 | 57154n3 | \([1, 1, 1, -173178, -27807037]\) | \(120920208625/19652\) | \(93349048544132\) | \([2]\) | \(414720\) | \(1.6897\) | |
| 57154.o1 | 57154n4 | \([1, 1, 1, -189988, -22105085]\) | \(159661140625/48275138\) | \(229311937748660258\) | \([2]\) | \(829440\) | \(2.0363\) |
Rank
sage: E.rank()
The elliptic curves in class 57154n have rank \(1\).
Complex multiplication
The elliptic curves in class 57154n do not have complex multiplication.Modular form 57154.2.a.n
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
