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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 102960e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 102960.m2 | 102960e1 | \([0, 0, 0, -8343, 2693142]\) | \(-12745567728/614453125\) | \(-3096135900000000\) | \([2]\) | \(442368\) | \(1.6524\) | \(\Gamma_0(N)\)-optimal |
| 102960.m1 | 102960e2 | \([0, 0, 0, -345843, 77820642]\) | \(226970509441932/1546455625\) | \(31169419332480000\) | \([2]\) | \(884736\) | \(1.9990\) |
Rank
sage: E.rank()
The elliptic curves in class 102960e have rank \(1\).
Complex multiplication
The elliptic curves in class 102960e do not have complex multiplication.Modular form 102960.2.a.e
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 Cremona 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 Cremona labels.
