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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 415794c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
415794.c4 | 415794c1 | \([1, 1, 0, -15616, -118784]\) | \(2845178713/1609728\) | \(238297515528192\) | \([2]\) | \(1824768\) | \(1.4487\) | \(\Gamma_0(N)\)-optimal |
415794.c2 | 415794c2 | \([1, 1, 0, -184896, -30623040]\) | \(4722184089433/9884736\) | \(1463295681290304\) | \([2, 2]\) | \(3649536\) | \(1.7953\) | |
415794.c3 | 415794c3 | \([1, 1, 0, -121416, -51888840]\) | \(-1337180541913/7067998104\) | \(-1046317382775954456\) | \([2]\) | \(7299072\) | \(2.1418\) | |
415794.c1 | 415794c4 | \([1, 1, 0, -2956856, -1958244024]\) | \(19312898130234073/84888\) | \(12566470545432\) | \([2]\) | \(7299072\) | \(2.1418\) |
Rank
sage: E.rank()
The elliptic curves in class 415794c have rank \(1\).
Complex multiplication
The elliptic curves in class 415794c do not have complex multiplication.Modular form 415794.2.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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.