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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 9675.p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 9675.p1 | 9675c2 | \([1, -1, 0, -31250067, -67231698534]\) | \(8000051600110940079507/144453125\) | \(60941162109375\) | \([2]\) | \(430080\) | \(2.6360\) | |
| 9675.p2 | 9675c1 | \([1, -1, 0, -1953192, -1050057909]\) | \(1953326569433829507/262451171875\) | \(110721588134765625\) | \([2]\) | \(215040\) | \(2.2894\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 9675.p have rank \(0\).
Complex multiplication
The elliptic curves in class 9675.p do not have complex multiplication.Modular form 9675.2.a.p
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.
