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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 270504.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 270504.n1 | 270504n4 | \([0, 0, 0, -36789411, -85887975314]\) | \(305612563186948/663\) | \(11946330943552512\) | \([2]\) | \(14155776\) | \(2.7588\) | |
| 270504.n2 | 270504n3 | \([0, 0, 0, -2976411, -487968986]\) | \(161838334948/87947613\) | \(1584692745993184269312\) | \([2]\) | \(14155776\) | \(2.7588\) | |
| 270504.n3 | 270504n2 | \([0, 0, 0, -2300151, -1341003350]\) | \(298766385232/439569\) | \(1980104353893828864\) | \([2, 2]\) | \(7077888\) | \(2.4122\) | |
| 270504.n4 | 270504n1 | \([0, 0, 0, -102306, -33285575]\) | \(-420616192/1456611\) | \(-410095141921638576\) | \([4]\) | \(3538944\) | \(2.0656\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 270504.n have rank \(1\).
Complex multiplication
The elliptic curves in class 270504.n do not have complex multiplication.Modular form 270504.2.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 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.
