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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 34496v
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 34496.cx2 | 34496v1 | \([0, -1, 0, 10911, -1668127]\) | \(4657463/41503\) | \(-1279993170362368\) | \([2]\) | \(147456\) | \(1.5801\) | \(\Gamma_0(N)\)-optimal |
| 34496.cx1 | 34496v2 | \([0, -1, 0, -161569, -23021151]\) | \(15124197817/1294139\) | \(39912514312208384\) | \([2]\) | \(294912\) | \(1.9267\) |
Rank
sage: E.rank()
The elliptic curves in class 34496v have rank \(0\).
Complex multiplication
The elliptic curves in class 34496v do not have complex multiplication.Modular form 34496.2.a.v
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.
