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SageMath
E = EllipticCurve("mg1")
E.isogeny_class()
Elliptic curves in class 352800.mg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 352800.mg1 | 352800mg2 | \([0, 0, 0, -1125211503675, 459408851879773250]\) | \(229625675762164624948320008/9568125\) | \(6564967731945000000000\) | \([2]\) | \(1981808640\) | \(5.0870\) | |
| 352800.mg2 | 352800mg4 | \([0, 0, 0, -70566894300, 7126549533992000]\) | \(7079962908642659949376/100085966990454375\) | \(549375049939540209358680000000000\) | \([2]\) | \(1981808640\) | \(5.0870\) | |
| 352800.mg3 | 352800mg1 | \([0, 0, 0, -70325722425, 7178262572117000]\) | \(448487713888272974160064/91549016015625\) | \(7851803985027031640625000000\) | \([2, 2]\) | \(990904320\) | \(4.7404\) | \(\Gamma_0(N)\)-optimal |
| 352800.mg4 | 352800mg3 | \([0, 0, 0, -70084605675, 7229928345956750]\) | \(-55486311952875723077768/801237030029296875\) | \(-549751936537386474609375000000000\) | \([2]\) | \(1981808640\) | \(5.0870\) |
Rank
sage: E.rank()
The elliptic curves in class 352800.mg have rank \(0\).
Complex multiplication
The elliptic curves in class 352800.mg do not have complex multiplication.Modular form 352800.2.a.mg
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.
