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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 2394.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2394.i1 | 2394j2 | \([1, -1, 1, -1355, -18849]\) | \(377149515625/90972\) | \(66318588\) | \([2]\) | \(1024\) | \(0.48980\) | |
2394.i2 | 2394j1 | \([1, -1, 1, -95, -201]\) | \(128787625/44688\) | \(32577552\) | \([2]\) | \(512\) | \(0.14323\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2394.i have rank \(1\).
Complex multiplication
The elliptic curves in class 2394.i do not have complex multiplication.Modular form 2394.2.a.i
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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.