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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 30912a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 30912.x3 | 30912a1 | \([0, -1, 0, -372, -1122]\) | \(89194791232/41136627\) | \(2632744128\) | \([2]\) | \(15360\) | \(0.50232\) | \(\Gamma_0(N)\)-optimal |
| 30912.x2 | 30912a2 | \([0, -1, 0, -3017, 63945]\) | \(741709148608/11431161\) | \(46822035456\) | \([2, 2]\) | \(30720\) | \(0.84890\) | |
| 30912.x4 | 30912a3 | \([0, -1, 0, -257, 173793]\) | \(-57512456/397771269\) | \(-13034168942592\) | \([2]\) | \(61440\) | \(1.1955\) | |
| 30912.x1 | 30912a4 | \([0, -1, 0, -48097, 4076065]\) | \(375523199368136/91287\) | \(2991292416\) | \([2]\) | \(61440\) | \(1.1955\) |
Rank
sage: E.rank()
The elliptic curves in class 30912a have rank \(1\).
Complex multiplication
The elliptic curves in class 30912a do not have complex multiplication.Modular form 30912.2.a.a
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
