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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 15456p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 15456.e3 | 15456p1 | \([0, -1, 0, -754, -7616]\) | \(741709148608/11431161\) | \(731594304\) | \([2, 2]\) | \(7680\) | \(0.50232\) | \(\Gamma_0(N)\)-optimal |
| 15456.e1 | 15456p2 | \([0, -1, 0, -12024, -503496]\) | \(375523199368136/91287\) | \(46738944\) | \([2]\) | \(15360\) | \(0.84890\) | |
| 15456.e2 | 15456p3 | \([0, -1, 0, -1489, 10465]\) | \(89194791232/41136627\) | \(168495624192\) | \([4]\) | \(15360\) | \(0.84890\) | |
| 15456.e4 | 15456p4 | \([0, -1, 0, -64, -21692]\) | \(-57512456/397771269\) | \(-203658889728\) | \([2]\) | \(15360\) | \(0.84890\) |
Rank
sage: E.rank()
The elliptic curves in class 15456p have rank \(0\).
Complex multiplication
The elliptic curves in class 15456p do not have complex multiplication.Modular form 15456.2.a.p
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
