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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 215475.x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 215475.x1 | 215475bh2 | \([0, -1, 1, -250683, -48252982]\) | \(-23100424192/14739\) | \(-1111599028921875\) | \([]\) | \(1516320\) | \(1.8280\) | |
| 215475.x2 | 215475bh1 | \([0, -1, 1, 2817, -278107]\) | \(32768/459\) | \(-34617270796875\) | \([]\) | \(505440\) | \(1.2787\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 215475.x have rank \(0\).
Complex multiplication
The elliptic curves in class 215475.x do not have complex multiplication.Modular form 215475.2.a.x
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
