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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 15059.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
15059.e1 | 15059e3 | \([0, -1, 1, -10706036, -13479575637]\) | \(-52893159101157376/11\) | \(-28222990499\) | \([]\) | \(258300\) | \(2.3022\) | |
15059.e2 | 15059e2 | \([0, -1, 1, -14146, -1168277]\) | \(-122023936/161051\) | \(-413212803895859\) | \([]\) | \(51660\) | \(1.4974\) | |
15059.e3 | 15059e1 | \([0, -1, 1, -456, 9063]\) | \(-4096/11\) | \(-28222990499\) | \([]\) | \(10332\) | \(0.69273\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 15059.e have rank \(0\).
Complex multiplication
The elliptic curves in class 15059.e do not have complex multiplication.Modular form 15059.2.a.e
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.