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SageMath
E = EllipticCurve("ec1")
E.isogeny_class()
Elliptic curves in class 102960.ec
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 102960.ec1 | 102960ec2 | \([0, 0, 0, -4222947, -3340192286]\) | \(2789222297765780449/677605500\) | \(2023319181312000\) | \([2]\) | \(1769472\) | \(2.3142\) | |
| 102960.ec2 | 102960ec1 | \([0, 0, 0, -262947, -52600286]\) | \(-673350049820449/10617750000\) | \(-31704431616000000\) | \([2]\) | \(884736\) | \(1.9676\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 102960.ec have rank \(1\).
Complex multiplication
The elliptic curves in class 102960.ec do not have complex multiplication.Modular form 102960.2.a.ec
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.
