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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 57222.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 57222.m1 | 57222s3 | \([1, -1, 0, -43162471422, 3451508339468692]\) | \(505384091400037554067434625/815656731648\) | \(14352530596901233026048\) | \([2]\) | \(79626240\) | \(4.4069\) | |
| 57222.m2 | 57222s4 | \([1, -1, 0, -43162055262, 3451578223802548]\) | \(-505369473241574671219626625/20303219722982711328\) | \(-357261297532543282674790909728\) | \([2]\) | \(159252480\) | \(4.7534\) | |
| 57222.m3 | 57222s1 | \([1, -1, 0, -534370302, 4706697104788]\) | \(959024269496848362625/11151660319506432\) | \(196227824441026791742636032\) | \([2]\) | \(26542080\) | \(3.8576\) | \(\Gamma_0(N)\)-optimal |
| 57222.m4 | 57222s2 | \([1, -1, 0, -108222462, 12006524374420]\) | \(-7966267523043306625/3534510366354604032\) | \(-62194261641993559768467013632\) | \([2]\) | \(53084160\) | \(4.2041\) |
Rank
sage: E.rank()
The elliptic curves in class 57222.m have rank \(1\).
Complex multiplication
The elliptic curves in class 57222.m do not have complex multiplication.Modular form 57222.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
