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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 377520q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 377520.q1 | 377520q1 | \([0, -1, 0, -68832221, 282179977521]\) | \(-5431655920328704/2036310046875\) | \(-13521059406100246572000000\) | \([]\) | \(82114560\) | \(3.5321\) | \(\Gamma_0(N)\)-optimal |
| 377520.q2 | 377520q2 | \([0, -1, 0, 525006739, -2879181109935]\) | \(2410191378353217536/1934051513671875\) | \(-12842064719440429687500000000\) | \([]\) | \(246343680\) | \(4.0814\) |
Rank
sage: E.rank()
The elliptic curves in class 377520q have rank \(1\).
Complex multiplication
The elliptic curves in class 377520q do not have complex multiplication.Modular form 377520.2.a.q
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
