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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 72897a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 72897.a3 | 72897a1 | \([1, 1, 0, -14404, 653827]\) | \(30664297/297\) | \(3201426952713\) | \([2]\) | \(154560\) | \(1.2193\) | \(\Gamma_0(N)\)-optimal |
| 72897.a2 | 72897a2 | \([1, 1, 0, -25449, -501480]\) | \(169112377/88209\) | \(950823804955761\) | \([2, 2]\) | \(309120\) | \(1.5659\) | |
| 72897.a4 | 72897a3 | \([1, 1, 0, 96046, -3781845]\) | \(9090072503/5845851\) | \(-63013686710249979\) | \([2]\) | \(618240\) | \(1.9124\) | |
| 72897.a1 | 72897a4 | \([1, 1, 0, -323664, -70939863]\) | \(347873904937/395307\) | \(4261099274061003\) | \([2]\) | \(618240\) | \(1.9124\) |
Rank
sage: E.rank()
The elliptic curves in class 72897a have rank \(0\).
Complex multiplication
The elliptic curves in class 72897a do not have complex multiplication.Modular form 72897.2.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.
