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SageMath
E = EllipticCurve("eh1")
E.isogeny_class()
Elliptic curves in class 102960.eh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 102960.eh1 | 102960cn2 | \([0, 0, 0, -3241107, 2245882194]\) | \(46703838741180867/148720000\) | \(11990039592960000\) | \([2]\) | \(1548288\) | \(2.3098\) | |
| 102960.eh2 | 102960cn1 | \([0, 0, 0, -199827, 36088146]\) | \(-10945484159427/644300800\) | \(-51944540759654400\) | \([2]\) | \(774144\) | \(1.9633\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 102960.eh have rank \(0\).
Complex multiplication
The elliptic curves in class 102960.eh do not have complex multiplication.Modular form 102960.2.a.eh
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.
