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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 15246.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 15246.m1 | 15246i6 | \([1, -1, 0, -2973537, -1972852227]\) | \(2251439055699625/25088\) | \(32400348406272\) | \([2]\) | \(207360\) | \(2.1614\) | |
| 15246.m2 | 15246i5 | \([1, -1, 0, -185697, -30842883]\) | \(-548347731625/1835008\) | \(-2369854054858752\) | \([2]\) | \(103680\) | \(1.8148\) | |
| 15246.m3 | 15246i4 | \([1, -1, 0, -38682, -2390580]\) | \(4956477625/941192\) | \(1215519320679048\) | \([2]\) | \(69120\) | \(1.6120\) | |
| 15246.m4 | 15246i2 | \([1, -1, 0, -11457, 474579]\) | \(128787625/98\) | \(126563860962\) | \([2]\) | \(23040\) | \(1.0627\) | |
| 15246.m5 | 15246i1 | \([1, -1, 0, -567, 10665]\) | \(-15625/28\) | \(-36161103132\) | \([2]\) | \(11520\) | \(0.71617\) | \(\Gamma_0(N)\)-optimal |
| 15246.m6 | 15246i3 | \([1, -1, 0, 4878, -221292]\) | \(9938375/21952\) | \(-28350304855488\) | \([2]\) | \(34560\) | \(1.2655\) |
Rank
sage: E.rank()
The elliptic curves in class 15246.m have rank \(1\).
Complex multiplication
The elliptic curves in class 15246.m do not have complex multiplication.Modular form 15246.2.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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 3 & 9 & 18 & 6 \\ 2 & 1 & 6 & 18 & 9 & 3 \\ 3 & 6 & 1 & 3 & 6 & 2 \\ 9 & 18 & 3 & 1 & 2 & 6 \\ 18 & 9 & 6 & 2 & 1 & 3 \\ 6 & 3 & 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
