Show commands:
SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 275082.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
275082.c1 | 275082c2 | \([1, 1, 0, -8072359273, 279153831559789]\) | \(1236526859255318155975783969/38367061931916216\) | \(1805012229968560399906296\) | \([]\) | \(185812704\) | \(4.1587\) | |
275082.c2 | 275082c1 | \([1, 1, 0, -36802513, -85138182251]\) | \(117174888570509216929/1273887851544576\) | \(59931176271111788691456\) | \([]\) | \(26544672\) | \(3.1857\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 275082.c have rank \(0\).
Complex multiplication
The elliptic curves in class 275082.c do not have complex multiplication.Modular form 275082.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.