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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 24276k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 24276.h1 | 24276k1 | \([0, 1, 0, -97489, -11737264]\) | \(265327034368/297381\) | \(114848870508624\) | \([2]\) | \(103680\) | \(1.6119\) | \(\Gamma_0(N)\)-optimal |
| 24276.h2 | 24276k2 | \([0, 1, 0, -72924, -17770428]\) | \(-6940769488/18000297\) | \(-111227753179646208\) | \([2]\) | \(207360\) | \(1.9585\) |
Rank
sage: E.rank()
The elliptic curves in class 24276k have rank \(0\).
Complex multiplication
The elliptic curves in class 24276k do not have complex multiplication.Modular form 24276.2.a.k
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.
