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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 24255.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 24255.l1 | 24255bi4 | \([1, -1, 1, -936473, -344805478]\) | \(1058993490188089/13182390375\) | \(1130602487971485375\) | \([2]\) | \(442368\) | \(2.2739\) | |
| 24255.l2 | 24255bi2 | \([1, -1, 1, -109598, 5458772]\) | \(1697509118089/833765625\) | \(71508843479390625\) | \([2, 2]\) | \(221184\) | \(1.9273\) | |
| 24255.l3 | 24255bi1 | \([1, -1, 1, -89753, 10364456]\) | \(932288503609/779625\) | \(66865412084625\) | \([2]\) | \(110592\) | \(1.5807\) | \(\Gamma_0(N)\)-optimal |
| 24255.l4 | 24255bi3 | \([1, -1, 1, 399757, 41521106]\) | \(82375335041831/56396484375\) | \(-4836907702880859375\) | \([2]\) | \(442368\) | \(2.2739\) |
Rank
sage: E.rank()
The elliptic curves in class 24255.l have rank \(0\).
Complex multiplication
The elliptic curves in class 24255.l do not have complex multiplication.Modular form 24255.2.a.l
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 LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
