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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 109520.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 109520.m1 | 109520a4 | \([0, 0, 0, -146483, 21578178]\) | \(132304644/5\) | \(13136519214080\) | \([2]\) | \(405504\) | \(1.6032\) | |
| 109520.m2 | 109520a2 | \([0, 0, 0, -9583, 303918]\) | \(148176/25\) | \(16420649017600\) | \([2, 2]\) | \(202752\) | \(1.2567\) | |
| 109520.m3 | 109520a1 | \([0, 0, 0, -2738, -50653]\) | \(55296/5\) | \(205258112720\) | \([2]\) | \(101376\) | \(0.91010\) | \(\Gamma_0(N)\)-optimal |
| 109520.m4 | 109520a3 | \([0, 0, 0, 17797, 1722202]\) | \(237276/625\) | \(-1642064901760000\) | \([2]\) | \(405504\) | \(1.6032\) |
Rank
sage: E.rank()
The elliptic curves in class 109520.m have rank \(1\).
Complex multiplication
The elliptic curves in class 109520.m do not have complex multiplication.Modular form 109520.2.a.m
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
