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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 4998.v
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4998.v1 | 4998v2 | \([1, 0, 1, -63976925, -196967451544]\) | \(717647917494305598319/844621814448\) | \(34083536763861513936\) | \([2]\) | \(451584\) | \(3.0307\) | |
| 4998.v2 | 4998v1 | \([1, 0, 1, -3965645, -3131017144]\) | \(-170915990723796079/6015674034432\) | \(-242754145825573396224\) | \([2]\) | \(225792\) | \(2.6841\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4998.v have rank \(0\).
Complex multiplication
The elliptic curves in class 4998.v do not have complex multiplication.Modular form 4998.2.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.
