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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 234416x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 234416.x2 | 234416x1 | \([0, 0, 0, -1715, 2924418]\) | \(-13500/89401\) | \(-3694236487072768\) | \([2]\) | \(1060864\) | \(1.6660\) | \(\Gamma_0(N)\)-optimal |
| 234416.x1 | 234416x2 | \([0, 0, 0, -317275, 67866666]\) | \(42738468750/656903\) | \(54289214462199808\) | \([2]\) | \(2121728\) | \(2.0126\) |
Rank
sage: E.rank()
The elliptic curves in class 234416x have rank \(0\).
Complex multiplication
The elliptic curves in class 234416x do not have complex multiplication.Modular form 234416.2.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 Cremona 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 Cremona labels.
