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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 6300.e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 6300.e1 | 6300i2 | \([0, 0, 0, -885, 10145]\) | \(-262885120/343\) | \(-100018800\) | \([]\) | \(2592\) | \(0.44213\) | |
| 6300.e2 | 6300i1 | \([0, 0, 0, 15, 65]\) | \(1280/7\) | \(-2041200\) | \([]\) | \(864\) | \(-0.10718\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 6300.e have rank \(1\).
Complex multiplication
The elliptic curves in class 6300.e do not have complex multiplication.Modular form 6300.2.a.e
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.
