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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 298116.v
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 298116.v1 | 298116v2 | \([0, 0, 0, -67431, -6243874]\) | \(109744/9\) | \(2780764669492992\) | \([2]\) | \(1658880\) | \(1.7060\) | |
| 298116.v2 | 298116v1 | \([0, 0, 0, -14196, 538265]\) | \(16384/3\) | \(57932597281104\) | \([2]\) | \(829440\) | \(1.3594\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 298116.v have rank \(0\).
Complex multiplication
The elliptic curves in class 298116.v do not have complex multiplication.Modular form 298116.2.a.v
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
