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SageMath
E = EllipticCurve("mr1")
E.isogeny_class()
Elliptic curves in class 235200mr
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 235200.mr4 | 235200mr1 | \([0, -1, 0, -3601908, 10956538062]\) | \(-43927191786304/415283203125\) | \(-48857653564453125000000\) | \([2]\) | \(17694720\) | \(3.0360\) | \(\Gamma_0(N)\)-optimal |
| 235200.mr3 | 235200mr2 | \([0, -1, 0, -99305033, 379892084937]\) | \(14383655824793536/45209390625\) | \(340405734249000000000000\) | \([2, 2]\) | \(35389440\) | \(3.3826\) | |
| 235200.mr1 | 235200mr3 | \([0, -1, 0, -1587680033, 24350171459937]\) | \(7347751505995469192/72930375\) | \(4393055072448000000000\) | \([2]\) | \(70778880\) | \(3.7291\) | |
| 235200.mr2 | 235200mr4 | \([0, -1, 0, -142180033, 19956459937]\) | \(5276930158229192/3050936350875\) | \(183777080700975552000000000\) | \([2]\) | \(70778880\) | \(3.7291\) |
Rank
sage: E.rank()
The elliptic curves in class 235200mr have rank \(0\).
Complex multiplication
The elliptic curves in class 235200mr do not have complex multiplication.Modular form 235200.2.a.mr
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 Cremona 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 Cremona labels.
