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SageMath
E = EllipticCurve("dz1")
E.isogeny_class()
Elliptic curves in class 102960.dz
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 102960.dz1 | 102960be2 | \([0, 0, 0, -672693267, 6667933317874]\) | \(22548490527122525577915938/183925440576065170125\) | \(274599211376540690475264000\) | \([2]\) | \(38338560\) | \(3.8998\) | |
| 102960.dz2 | 102960be1 | \([0, 0, 0, -13848267, 241690956874]\) | \(-393443624385770851876/33577011001321734375\) | \(-25065104404442669424000000\) | \([2]\) | \(19169280\) | \(3.5532\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 102960.dz have rank \(1\).
Complex multiplication
The elliptic curves in class 102960.dz do not have complex multiplication.Modular form 102960.2.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.
