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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 24048k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 24048.k2 | 24048k1 | \([0, 0, 0, 357, -1910]\) | \(1685159/1503\) | \(-4487933952\) | \([2]\) | \(23552\) | \(0.53946\) | \(\Gamma_0(N)\)-optimal |
| 24048.k1 | 24048k2 | \([0, 0, 0, -1803, -17030]\) | \(217081801/83667\) | \(249828323328\) | \([2]\) | \(47104\) | \(0.88604\) |
Rank
sage: E.rank()
The elliptic curves in class 24048k have rank \(0\).
Complex multiplication
The elliptic curves in class 24048k do not have complex multiplication.Modular form 24048.2.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.
