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SageMath
E = EllipticCurve("en1")
E.isogeny_class()
Elliptic curves in class 102960en
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 102960.es3 | 102960en1 | \([0, 0, 0, -9507, -258014]\) | \(31824875809/8785920\) | \(26234616545280\) | \([2]\) | \(221184\) | \(1.2823\) | \(\Gamma_0(N)\)-optimal |
| 102960.es2 | 102960en2 | \([0, 0, 0, -55587, 4838434]\) | \(6361447449889/294465600\) | \(879269570150400\) | \([2, 2]\) | \(442368\) | \(1.6289\) | |
| 102960.es4 | 102960en3 | \([0, 0, 0, 30813, 18506914]\) | \(1083523132511/50179392120\) | \(-149834862000046080\) | \([2]\) | \(884736\) | \(1.9755\) | |
| 102960.es1 | 102960en4 | \([0, 0, 0, -879267, 317342626]\) | \(25176685646263969/57915000\) | \(172933263360000\) | \([2]\) | \(884736\) | \(1.9755\) |
Rank
sage: E.rank()
The elliptic curves in class 102960en have rank \(1\).
Complex multiplication
The elliptic curves in class 102960en do not have complex multiplication.Modular form 102960.2.a.en
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.
