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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 90354.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 90354.m1 | 90354l4 | \([1, 1, 1, -659946329, 4313767086311]\) | \(244587381607181341/79679768374272\) | \(10355321324389143178719058944\) | \([2]\) | \(85248000\) | \(4.0788\) | |
| 90354.m2 | 90354l2 | \([1, 1, 1, -262573544, -1637772491059]\) | \(15404978391891661/117612\) | \(15285060140778596124\) | \([2]\) | \(17049600\) | \(3.2741\) | |
| 90354.m3 | 90354l1 | \([1, 1, 1, -16399964, -25630950355]\) | \(-3753503985421/10392624\) | \(-1350643496076072312048\) | \([2]\) | \(8524800\) | \(2.9275\) | \(\Gamma_0(N)\)-optimal |
| 90354.m4 | 90354l3 | \([1, 1, 1, 118083751, 461895766247]\) | \(1401130594505699/1519867920384\) | \(-197524679191830214311149568\) | \([2]\) | \(42624000\) | \(3.7323\) |
Rank
sage: E.rank()
The elliptic curves in class 90354.m have rank \(1\).
Complex multiplication
The elliptic curves in class 90354.m do not have complex multiplication.Modular form 90354.2.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.
\(\left(\begin{array}{rrrr} 1 & 5 & 10 & 2 \\ 5 & 1 & 2 & 10 \\ 10 & 2 & 1 & 5 \\ 2 & 10 & 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
