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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 95139k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 95139.k3 | 95139k1 | \([0, 0, 1, -2883, 141507]\) | \(-4096/11\) | \(-7116892017939\) | \([]\) | \(175500\) | \(1.1536\) | \(\Gamma_0(N)\)-optimal |
| 95139.k2 | 95139k2 | \([0, 0, 1, -89373, -18626823]\) | \(-122023936/161051\) | \(-104198416034644899\) | \([]\) | \(877500\) | \(1.9583\) | |
| 95139.k1 | 95139k3 | \([0, 0, 1, -67638063, -214108967133]\) | \(-52893159101157376/11\) | \(-7116892017939\) | \([]\) | \(4387500\) | \(2.7630\) |
Rank
sage: E.rank()
The elliptic curves in class 95139k have rank \(0\).
Complex multiplication
The elliptic curves in class 95139k do not have complex multiplication.Modular form 95139.2.a.k
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 Cremona 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 Cremona labels.
