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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 35378k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
35378.m2 | 35378k1 | \([1, -1, 1, 987267, -11034187867]\) | \(53261199/26353376\) | \(-52656659719276466165984\) | \([]\) | \(2298240\) | \(3.0389\) | \(\Gamma_0(N)\)-optimal |
35378.m1 | 35378k2 | \([1, -1, 1, -1340015823, 18910251211415]\) | \(-133179212896925841/240518168576\) | \(-480579162191971378773622784\) | \([]\) | \(16087680\) | \(4.0119\) |
Rank
sage: E.rank()
The elliptic curves in class 35378k have rank \(1\).
Complex multiplication
The elliptic curves in class 35378k do not have complex multiplication.Modular form 35378.2.a.k
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.