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SageMath
sage: E = EllipticCurve("x1")
sage: E.isogeny_class()
Elliptic curves in class 348726.x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 348726.x1 | 348726x1 | \([1, 0, 1, -548006, -145152520]\) | \(56402207875/4451328\) | \(1436388784379200512\) | \([2]\) | \(5836800\) | \(2.2278\) | \(\Gamma_0(N)\)-optimal |
| 348726.x2 | 348726x2 | \([1, 0, 1, 549434, -653486728]\) | \(56844576125/604685088\) | \(-195124438928012019552\) | \([2]\) | \(11673600\) | \(2.5744\) |
Rank
sage: E.rank()
The elliptic curves in class 348726.x have rank \(1\).
Complex multiplication
The elliptic curves in class 348726.x do not have complex multiplication.Modular form 348726.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
