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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 3150.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3150.k1 | 3150g2 | \([1, -1, 0, -36492, 2690666]\) | \(139798359/98\) | \(3767449218750\) | \([2]\) | \(11520\) | \(1.3495\) | |
| 3150.k2 | 3150g1 | \([1, -1, 0, -2742, 24416]\) | \(59319/28\) | \(1076414062500\) | \([2]\) | \(5760\) | \(1.0029\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3150.k have rank \(0\).
Complex multiplication
The elliptic curves in class 3150.k do not have complex multiplication.Modular form 3150.2.a.k
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.
