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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 35280.r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 35280.r1 | 35280ek3 | \([0, 0, 0, -926688, 359184112]\) | \(-250523582464/13671875\) | \(-4802902776000000000\) | \([]\) | \(622080\) | \(2.3429\) | |
| 35280.r2 | 35280ek1 | \([0, 0, 0, -9408, -389648]\) | \(-262144/35\) | \(-12295431106560\) | \([]\) | \(69120\) | \(1.2443\) | \(\Gamma_0(N)\)-optimal |
| 35280.r3 | 35280ek2 | \([0, 0, 0, 61152, 993328]\) | \(71991296/42875\) | \(-15061903105536000\) | \([]\) | \(207360\) | \(1.7936\) |
Rank
sage: E.rank()
The elliptic curves in class 35280.r have rank \(0\).
Complex multiplication
The elliptic curves in class 35280.r do not have complex multiplication.Modular form 35280.2.a.r
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.
\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
