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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 389376q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 389376.q4 | 389376q1 | \([0, 0, 0, 1014, 193336]\) | \(64/9\) | \(-16214371250688\) | \([2]\) | \(552960\) | \(1.2141\) | \(\Gamma_0(N)\)-optimal |
| 389376.q3 | 389376q2 | \([0, 0, 0, -44616, 3515200]\) | \(85184/3\) | \(345906586681344\) | \([2]\) | \(1105920\) | \(1.5606\) | |
| 389376.q2 | 389376q3 | \([0, 0, 0, -242346, -48527336]\) | \(-873722816/59049\) | \(-106382489775763968\) | \([2]\) | \(2764800\) | \(2.0188\) | |
| 389376.q1 | 389376q4 | \([0, 0, 0, -3938376, -3008308160]\) | \(58591911104/243\) | \(28018433521188864\) | \([2]\) | \(5529600\) | \(2.3654\) |
Rank
sage: E.rank()
The elliptic curves in class 389376q have rank \(1\).
Complex multiplication
The elliptic curves in class 389376q do not have complex multiplication.Modular form 389376.2.a.q
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
