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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 61152.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 61152.l1 | 61152b2 | \([0, -1, 0, -64353, -6258447]\) | \(61162984000/41067\) | \(19789789114368\) | \([2]\) | \(230400\) | \(1.4898\) | |
| 61152.l2 | 61152b1 | \([0, -1, 0, -4818, -54900]\) | \(1643032000/767637\) | \(5779950426432\) | \([2]\) | \(115200\) | \(1.1432\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 61152.l have rank \(0\).
Complex multiplication
The elliptic curves in class 61152.l do not have complex multiplication.Modular form 61152.2.a.l
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
