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SageMath
E = EllipticCurve("es1")
E.isogeny_class()
Elliptic curves in class 35280.es
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
35280.es1 | 35280ff4 | \([0, 0, 0, -793947, 272272714]\) | \(157551496201/13125\) | \(4610786664960000\) | \([4]\) | \(393216\) | \(2.0494\) | |
35280.es2 | 35280ff2 | \([0, 0, 0, -53067, 3629626]\) | \(47045881/11025\) | \(3873060798566400\) | \([2, 2]\) | \(196608\) | \(1.7029\) | |
35280.es3 | 35280ff1 | \([0, 0, 0, -17787, -865046]\) | \(1771561/105\) | \(36886293319680\) | \([2]\) | \(98304\) | \(1.3563\) | \(\Gamma_0(N)\)-optimal |
35280.es4 | 35280ff3 | \([0, 0, 0, 123333, 22645546]\) | \(590589719/972405\) | \(-341603962433556480\) | \([2]\) | \(393216\) | \(2.0494\) |
Rank
sage: E.rank()
The elliptic curves in class 35280.es have rank \(1\).
Complex multiplication
The elliptic curves in class 35280.es do not have complex multiplication.Modular form 35280.2.a.es
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.