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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 121242f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 121242.h1 | 121242f1 | \([1, 0, 1, -39372, 2993494]\) | \(5070983873798627/19761810732\) | \(26302970084292\) | \([2]\) | \(405504\) | \(1.4329\) | \(\Gamma_0(N)\)-optimal |
| 121242.h2 | 121242f2 | \([1, 0, 1, -21002, 5800430]\) | \(-769658186424707/10481273909406\) | \(-13950575573419386\) | \([2]\) | \(811008\) | \(1.7794\) |
Rank
sage: E.rank()
The elliptic curves in class 121242f have rank \(2\).
Complex multiplication
The elliptic curves in class 121242f do not have complex multiplication.Modular form 121242.2.a.f
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.
