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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 13566.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 13566.m1 | 13566l3 | \([1, 1, 1, -40044, -3082113]\) | \(7101281816103496897/50099889941262\) | \(50099889941262\) | \([2]\) | \(79872\) | \(1.4614\) | |
| 13566.m2 | 13566l2 | \([1, 1, 1, -4134, 20511]\) | \(7813429445648737/4308107057604\) | \(4308107057604\) | \([2, 2]\) | \(39936\) | \(1.1149\) | |
| 13566.m3 | 13566l1 | \([1, 1, 1, -3154, 66767]\) | \(3469903405095457/5695440912\) | \(5695440912\) | \([4]\) | \(19968\) | \(0.76828\) | \(\Gamma_0(N)\)-optimal |
| 13566.m4 | 13566l4 | \([1, 1, 1, 16096, 182351]\) | \(461185788415532543/280217554681806\) | \(-280217554681806\) | \([2]\) | \(79872\) | \(1.4614\) |
Rank
sage: E.rank()
The elliptic curves in class 13566.m have rank \(1\).
Complex multiplication
The elliptic curves in class 13566.m do not have complex multiplication.Modular form 13566.2.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.
