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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 380926e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
380926.e2 | 380926e1 | \([1, 0, 1, -190636, -12007110]\) | \(391197625/194672\) | \(381278634135347312\) | \([3]\) | \(4447872\) | \(2.0665\) | \(\Gamma_0(N)\)-optimal |
380926.e1 | 380926e2 | \([1, 0, 1, -12570731, -17155962666]\) | \(112167304419625/94208\) | \(184512911793287168\) | \([]\) | \(13343616\) | \(2.6158\) |
Rank
sage: E.rank()
The elliptic curves in class 380926e have rank \(2\).
Complex multiplication
The elliptic curves in class 380926e do not have complex multiplication.Modular form 380926.2.a.e
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.