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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 94136d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 94136.e3 | 94136d1 | \([0, 0, 0, -1127951, 461081490]\) | \(130512259152/2009\) | \(2442997611563264\) | \([4]\) | \(806400\) | \(2.0879\) | \(\Gamma_0(N)\)-optimal |
| 94136.e2 | 94136d2 | \([0, 0, 0, -1161571, 432134670]\) | \(35633452068/4036081\) | \(19631928806522389504\) | \([2, 2]\) | \(1612800\) | \(2.4345\) | |
| 94136.e4 | 94136d3 | \([0, 0, 0, 1595269, 2172803446]\) | \(46152198846/236356841\) | \(-2299329808022451570688\) | \([2]\) | \(3225600\) | \(2.7811\) | |
| 94136.e1 | 94136d4 | \([0, 0, 0, -4456331, -3161130586]\) | \(1006057824354/138462289\) | \(1346990707092413745152\) | \([2]\) | \(3225600\) | \(2.7811\) |
Rank
sage: E.rank()
The elliptic curves in class 94136d have rank \(0\).
Complex multiplication
The elliptic curves in class 94136d do not have complex multiplication.Modular form 94136.2.a.d
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.
