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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 11424g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 11424.t2 | 11424g1 | \([0, 1, 0, 1458, 0]\) | \(5352028359488/3098832471\) | \(-198325278144\) | \([2]\) | \(11520\) | \(0.85723\) | \(\Gamma_0(N)\)-optimal |
| 11424.t1 | 11424g2 | \([0, 1, 0, -5832, -5832]\) | \(42852953779784/24786408969\) | \(12690641392128\) | \([2]\) | \(23040\) | \(1.2038\) |
Rank
sage: E.rank()
The elliptic curves in class 11424g have rank \(1\).
Complex multiplication
The elliptic curves in class 11424g do not have complex multiplication.Modular form 11424.2.a.g
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.
