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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 62530.a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 62530.a1 | 62530b3 | \([1, 0, 1, -891479, -324051414]\) | \(16232905099479601/4052240\) | \(19559388502160\) | \([2]\) | \(663552\) | \(1.9260\) | |
| 62530.a2 | 62530b4 | \([1, 0, 1, -888099, -326629678]\) | \(-16048965315233521/256572640900\) | \(-1238427132249888100\) | \([2]\) | \(1327104\) | \(2.2726\) | |
| 62530.a3 | 62530b1 | \([1, 0, 1, -12679, -301494]\) | \(46694890801/18944000\) | \(91439069696000\) | \([2]\) | \(221184\) | \(1.3767\) | \(\Gamma_0(N)\)-optimal |
| 62530.a4 | 62530b2 | \([1, 0, 1, 41401, -2183478]\) | \(1625964918479/1369000000\) | \(-6607901521000000\) | \([2]\) | \(442368\) | \(1.7232\) |
Rank
sage: E.rank()
The elliptic curves in class 62530.a have rank \(1\).
Complex multiplication
The elliptic curves in class 62530.a do not have complex multiplication.Modular form 62530.2.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 LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
