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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 2898.o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2898.o1 | 2898p4 | \([1, -1, 1, -13648415, 19316887175]\) | \(385693937170561837203625/2159357734550274048\) | \(1574171788487149780992\) | \([6]\) | \(230400\) | \(2.9097\) | |
| 2898.o2 | 2898p2 | \([1, -1, 1, -1007960, -370857157]\) | \(155355156733986861625/8291568305839392\) | \(6044553294956916768\) | \([2]\) | \(76800\) | \(2.3604\) | |
| 2898.o3 | 2898p3 | \([1, -1, 1, -377375, 636571271]\) | \(-8152944444844179625/235342826399858688\) | \(-171564920445496983552\) | \([6]\) | \(115200\) | \(2.5631\) | |
| 2898.o4 | 2898p1 | \([1, -1, 1, 41800, -23176645]\) | \(11079872671250375/324440155855872\) | \(-236516873618930688\) | \([2]\) | \(38400\) | \(2.0138\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2898.o have rank \(0\).
Complex multiplication
The elliptic curves in class 2898.o do not have complex multiplication.Modular form 2898.2.a.o
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 2 & 6 \\ 3 & 1 & 6 & 2 \\ 2 & 6 & 1 & 3 \\ 6 & 2 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
