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SageMath
E = EllipticCurve("dl1")
E.isogeny_class()
Elliptic curves in class 107712.dl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 107712.dl1 | 107712en4 | \([0, 0, 0, -808846284, -8854154695280]\) | \(306234591284035366263793/1727485056\) | \(330127535197126656\) | \([2]\) | \(16515072\) | \(3.4313\) | |
| 107712.dl2 | 107712en2 | \([0, 0, 0, -50553804, -138340930160]\) | \(74768347616680342513/5615307472896\) | \(1073101969225464938496\) | \([2, 2]\) | \(8257536\) | \(3.0847\) | |
| 107712.dl3 | 107712en3 | \([0, 0, 0, -47236044, -157282685552]\) | \(-60992553706117024753/20624795251201152\) | \(-3941459751895207721828352\) | \([2]\) | \(16515072\) | \(3.4313\) | |
| 107712.dl4 | 107712en1 | \([0, 0, 0, -3367884, -1860375152]\) | \(22106889268753393/4969545596928\) | \(949694952940637257728\) | \([2]\) | \(4128768\) | \(2.7381\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 107712.dl have rank \(0\).
Complex multiplication
The elliptic curves in class 107712.dl do not have complex multiplication.Modular form 107712.2.a.dl
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.
