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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 3675.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3675.c1 | 3675n2 | \([0, 1, 1, -22808, 1319294]\) | \(-1713910976512/1594323\) | \(-1220653546875\) | \([]\) | \(9984\) | \(1.2421\) | |
3675.c2 | 3675n1 | \([0, 1, 1, -58, -206]\) | \(-28672/3\) | \(-2296875\) | \([]\) | \(768\) | \(-0.040369\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3675.c have rank \(1\).
Complex multiplication
The elliptic curves in class 3675.c do not have complex multiplication.Modular form 3675.2.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.
\(\left(\begin{array}{rr} 1 & 13 \\ 13 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.