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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 273325l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
273325.l2 | 273325l1 | \([0, 1, 1, -2803, 52134]\) | \(163840/13\) | \(193317579325\) | \([]\) | \(299376\) | \(0.90922\) | \(\Gamma_0(N)\)-optimal |
273325.l1 | 273325l2 | \([0, 1, 1, -44853, -3660881]\) | \(671088640/2197\) | \(32670670905925\) | \([]\) | \(898128\) | \(1.4585\) |
Rank
sage: E.rank()
The elliptic curves in class 273325l have rank \(1\).
Complex multiplication
The elliptic curves in class 273325l do not have complex multiplication.Modular form 273325.2.a.l
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.