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SageMath
E = EllipticCurve("dz1")
E.isogeny_class()
Elliptic curves in class 90944.dz
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 90944.dz1 | 90944by2 | \([0, -1, 0, -7010593, -7142054751]\) | \(2471097448795250/98942809\) | \(1525746569843965952\) | \([2]\) | \(2359296\) | \(2.5720\) | |
| 90944.dz2 | 90944by1 | \([0, -1, 0, -417153, -122678527]\) | \(-1041220466500/242597383\) | \(-1870485226295590912\) | \([2]\) | \(1179648\) | \(2.2254\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 90944.dz have rank \(1\).
Complex multiplication
The elliptic curves in class 90944.dz do not have complex multiplication.Modular form 90944.2.a.dz
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.
