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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 34969.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
34969.m1 | 34969h3 | \([0, 1, 1, -273469236, 1740556342399]\) | \(-52893159101157376/11\) | \(-470372934627299\) | \([]\) | \(3072000\) | \(3.1123\) | |
34969.m2 | 34969h2 | \([0, 1, 1, -361346, 151310539]\) | \(-122023936/161051\) | \(-6886730135878284659\) | \([]\) | \(614400\) | \(2.3075\) | |
34969.m3 | 34969h1 | \([0, 1, 1, -11656, -1154301]\) | \(-4096/11\) | \(-470372934627299\) | \([]\) | \(122880\) | \(1.5028\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 34969.m have rank \(0\).
Complex multiplication
The elliptic curves in class 34969.m do not have complex multiplication.Modular form 34969.2.a.m
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.
\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.