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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 86394.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 86394.m1 | 86394d4 | \([1, 1, 0, -29516984, -61736587458]\) | \(1605401128026436521313/3820083498\) | \(6767510941800378\) | \([2]\) | \(4792320\) | \(2.7054\) | |
| 86394.m2 | 86394d3 | \([1, 1, 0, -2400884, -336759342]\) | \(863935691003495713/472472268071958\) | \(837013443697825986438\) | \([2]\) | \(4792320\) | \(2.7054\) | |
| 86394.m3 | 86394d2 | \([1, 1, 0, -1845494, -964461120]\) | \(392379113447076673/604577782116\) | \(1071046420263203076\) | \([2, 2]\) | \(2396160\) | \(2.3589\) | |
| 86394.m4 | 86394d1 | \([1, 1, 0, -81314, -24153180]\) | \(-33563861678593/122435503344\) | \(-216901962739599984\) | \([2]\) | \(1198080\) | \(2.0123\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 86394.m have rank \(1\).
Complex multiplication
The elliptic curves in class 86394.m do not have complex multiplication.Modular form 86394.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
