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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 5712.a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 5712.a1 | 5712m3 | \([0, -1, 0, -6107232, 5811414144]\) | \(-6150311179917589675873/244053849830826\) | \(-999644568907063296\) | \([]\) | \(233280\) | \(2.5373\) | |
| 5712.a2 | 5712m2 | \([0, -1, 0, -15552, 20169216]\) | \(-101566487155393/42823570577256\) | \(-175405345084440576\) | \([]\) | \(77760\) | \(1.9880\) | |
| 5712.a3 | 5712m1 | \([0, -1, 0, 1728, -746496]\) | \(139233463487/58763045376\) | \(-240693433860096\) | \([]\) | \(25920\) | \(1.4386\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 5712.a have rank \(0\).
Complex multiplication
The elliptic curves in class 5712.a do not have complex multiplication.Modular form 5712.2.a.a
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
