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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 23400.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 23400.l1 | 23400r2 | \([0, 0, 0, -963075, 254902750]\) | \(4234737878642/1247410125\) | \(29099583396000000000\) | \([2]\) | \(368640\) | \(2.4406\) | |
| 23400.l2 | 23400r1 | \([0, 0, 0, 161925, 26527750]\) | \(40254822716/49359375\) | \(-575727750000000000\) | \([2]\) | \(184320\) | \(2.0940\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 23400.l have rank \(1\).
Complex multiplication
The elliptic curves in class 23400.l do not have complex multiplication.Modular form 23400.2.a.l
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.
