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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 18515.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
18515.c1 | 18515h1 | \([1, 0, 0, -126, -245]\) | \(18191447/8575\) | \(104332025\) | \([2]\) | \(5184\) | \(0.23279\) | \(\Gamma_0(N)\)-optimal |
18515.c2 | 18515h2 | \([1, 0, 0, 449, -1740]\) | \(822656953/588245\) | \(-7157176915\) | \([2]\) | \(10368\) | \(0.57936\) |
Rank
sage: E.rank()
The elliptic curves in class 18515.c have rank \(1\).
Complex multiplication
The elliptic curves in class 18515.c do not have complex multiplication.Modular form 18515.2.a.c
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.