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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 79420.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 79420.c1 | 79420d2 | \([0, 1, 0, -40913075940, -3116674918567100]\) | \(628852131191469082134214096/15500412670233154296875\) | \(186683025903278392142187500000000\) | \([2]\) | \(433520640\) | \(4.9760\) | |
| 79420.c2 | 79420d1 | \([0, 1, 0, -5738732285, 96628001954308]\) | \(27767067707389964045910016/10710132025277343828125\) | \(8061881548087790555744851250000\) | \([2]\) | \(216760320\) | \(4.6294\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 79420.c have rank \(1\).
Complex multiplication
The elliptic curves in class 79420.c do not have complex multiplication.Modular form 79420.2.a.c
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.
