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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 318402.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 318402.f1 | 318402f2 | \([1, -1, 0, -302766, -64053172]\) | \(-67645179/8\) | \(-362993597683416\) | \([]\) | \(3079296\) | \(1.8193\) | |
| 318402.f2 | 318402f1 | \([1, -1, 0, 474, -271692]\) | \(189/512\) | \(-31867750688256\) | \([]\) | \(1026432\) | \(1.2700\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 318402.f have rank \(1\).
Complex multiplication
The elliptic curves in class 318402.f do not have complex multiplication.Modular form 318402.2.a.f
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
